the properties of galaxies in supercluster filamentsetheses.bham.ac.uk/986/1/porter07phd.pdfthe...

The properties of galaxies insupercluster filaments

byScott Clive Porter

A Thesis submitted to

The University of Birmingham

for the degree of

Doctor of Philosophy

Astrophysics and Space Research Group

School of Physics and Astronomy

University of Birmingham

England

October 2006

University of Birmingham Research Archive

e-theses repository This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder.

Synopsis

Superclusters appear as large-scale structures in the form of a network of fila-

ments, and can be up to 100 h−1100 Mpc in extent. In this dissertation, we investigate

in detail the spatial structure of the three richest superclusters of galaxies closer to

us then z=0.1.

We investigate the rate of star formation in galaxies at various positions among

the filaments and clusters in the Pisces-Cetus Supercluster. We use an index of star

formation derived from a principal component analysis of optical spectra. We have

shown that galaxies which are members of these filaments, show a steady decline in

star formation rate, from the periphery of a cluster, into the cluster core. However,

on top of this trend, we find a nearly instantaneous enhancement of the rate of star

formation at ∼ 3 h−170 Mpc from its centre. We conclude that the most likely reason

for this sudden enhancement in star formation rate is galaxy-galaxy harassment.

Further work shows that the enhancement in star formation occurs mainly in the

infalling dwarf galaxies (−20 < MB < −17.5) and that there is little evidence

that the tidal effect of the dark matter haloes of the clusters is responsible for the

enhanced star formation.

The results of an anaylsis performed on a larger ensemble of 52 filaments were

consistent with the those from our smaller sample drawn from the Pisces-Cetus

supercluster.

We conclude this study with the analysis of a sample of spectra from the 6dF

redshift survey. In the absence of spectrophotometric calibration, for these galaxies

we were only able to obtain an uncalibrated star formation rate, but we could

examine the effect of correction due to dust extinction, and could separate the star-

forming galaxies from the active galactic nuclei. From our small sample, there was

interesting evidence of enhanced star formation in galaxies at similar distances from

the centres of the clusters in the Shapley Supercluster.

Acknowledgements

Over the course of my PhD I have received help and support from a range of

people, but my foundation of strength has come from my parents as it has throughout

my life. They supported me both financially and emotionally throughout my degree

and PhD and have always encouraged without applying pressure. Without them I

would never have completed this work. I would also like to say a massive thank you

to my supervisor Dr Somak Raychaudhury for his constant support and inspiration.

He has always been able to pull me forwards when everything seemed to be going

wrong and re-light the fires of determination to continue. I am indebted to Philip

Lah for his contribution of 6dF spectroscopic data and Kevin Pimbblet for sharing

with us his work on filaments in the 2dFGRS. I am also grateful to Stuart Aston,

Stephen Fletcher and Robert Satchwell for their support and friendship which helped

pull me through my degree. Going further back I would like to thank my A level

mathematics teachers at Stourbridge College, Shangara Baines and Lhaktar Dhaga.

When others had told me to quit, they believed in me and their efforts, above and

beyond the call of duty, enabled me to continue my education. I would also like to

mention the other inhabitants of G27 and members of the extragalactic group for

their scientific advice and discussions on football and cricket which always lightened

a day of programming. Finally I would like to thank all the members of Astrosoc

over the years and the committee members I served with. They provided a much

needed distraction from the technical side of astrophysics and enabled me to see the

beauty of the Universe I was studying.

Publications

Publications in Refereed Journals

1. The Pisces-Cetus Supercluster a remarkable filament of galaxies in the 2dF

Galaxy Redshift and Sloan Digital Sky surveys: Scott C. Porter and Somak

Raychaudhury, 2005, MNRAS, 364, 1387-1396 (astro-ph/0511050). (This pa-

per is integrated into chapters 3 and 4)

2. Star formation in galaxies along the Pisces-Cetus Supercluster filaments: Scott

C. Porter and Somak Raychaudhury, 2006, MNRAS, accepted, (astro-ph/0612357).

(This paper is integrated into chapter 4)

3. Star formation properties of galaxies in supercluster filaments in the 2dF

Galaxy Redshift Survey: Scott C. Porter, Somak Raychaudhury and Kevin

A. Pimbblet, in preparation. (This paper is integrated into chapter 5) [Kevin

Pimbblet contributed the initial filament catalogue]

Publications in Contributed Conference Proceedings

1. The Pisces-Cetus Supercluster: the largest filament of galaxies in the 2dF-

GRS region, Scott C. Porter and Somak Raychaudhury 2004, abstract in the

proceedings of the RAS National Astronomy Meeting, Milton Keynes, April

2004.

2. Enhanced star formation in group galaxies in the Pisces-Cetus supercluster:

Scott C. Porter and Somak Raychaudhury, 2005, abstract in the proceedings

of the RAS National Astronomy Meeting, Birmingham, April 2005.

3. Star formation properties in Supercluster Filaments: Somak Raychaudhury

and Scott C. Porter, 2005, abstract, Bulletin of the American Astronomical

Society, 207, 177.15

Contents

1 Introduction 1

1.1 Structure formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.1.1 The power spectrum . . . . . . . . . . . . . . . . . . . . . . . 3

1.1.2 The growth of perturbations . . . . . . . . . . . . . . . . . . . 4

1.2 Dark matter and cosmological models . . . . . . . . . . . . . . . . . . 5

1.2.1 Hot Dark Matter . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.2.2 Warm Dark Matter . . . . . . . . . . . . . . . . . . . . . . . . 9

1.2.3 Cold Dark Matter with Dark Energy . . . . . . . . . . . . . . 9

1.2.4 Bias . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.2.5 Peculiar velocities . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.2.6 N-body simulations . . . . . . . . . . . . . . . . . . . . . . . . 11

1.3 The definition of a supercluster . . . . . . . . . . . . . . . . . . . . . 12

1.4 Observational Surveys . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.4.1 The Two Degree Galaxy Redshift Survey . . . . . . . . . . . . 14

1.4.2 The 2dFGRS Percolation-Inferred Galaxy Group catalogue . . 15

1.4.3 The Six degree Galaxy Survey . . . . . . . . . . . . . . . . . . 16

1.4.4 The Sloan Digital Sky Survey . . . . . . . . . . . . . . . . . . 17

1.4.5 Super COSMOS . . . . . . . . . . . . . . . . . . . . . . . . . . 18

1.5 Cosmology in this thesis . . . . . . . . . . . . . . . . . . . . . . . . . 18

1.6 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2 Star formation in galaxies 20

2.1 Star formation as a function of time . . . . . . . . . . . . . . . . . . . 20

2.2 Star formation as a function of environment . . . . . . . . . . . . . . 22

v

Contents vi

2.3 Star formation indicators . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.3.1 Recombination lines of Hydrogen . . . . . . . . . . . . . . . . 23

2.3.2 Ultraviolet continuum emission from hot stars . . . . . . . . . 25

2.3.3 Infrared thermal emission . . . . . . . . . . . . . . . . . . . . 26

2.3.4 X-ray Luminosity . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.4 Star formation in interacting galaxies . . . . . . . . . . . . . . . . . . 27

2.4.1 Star formation mechanisms . . . . . . . . . . . . . . . . . . . 27

2.4.2 Environmental influences . . . . . . . . . . . . . . . . . . . . . 29

2.5 A star formation index from 2dFGRS spectra: the η parameter . . . . 33

2.5.1 The Principal Component Analysis . . . . . . . . . . . . . . . 33

2.5.2 Relationships with other parameters . . . . . . . . . . . . . . 34

2.5.3 Separating the star-forming and non star-forming populations 38

3 Supercluster structure 42

3.1 Minimal spanning tree supercluster structure . . . . . . . . . . . . . . 42

3.1.1 The Pisces-Cetus supercluster . . . . . . . . . . . . . . . . . . 43

3.1.2 The Horologium-Reticulum Supercluster . . . . . . . . . . . . 46

3.1.3 The Shapley supercluster . . . . . . . . . . . . . . . . . . . . . 52

3.2 Mean redshift and velocity dispersion . . . . . . . . . . . . . . . . . . 54

3.2.1 Models of Surface brightness . . . . . . . . . . . . . . . . . . . 56

3.3 Virial mass estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

3.4 A lower limit to the Mass of the Superclusters . . . . . . . . . . . . . 71

3.4.1 Pisces-Cetus supercluster . . . . . . . . . . . . . . . . . . . . . 71

3.4.2 Horologium-Reticulum supercluster . . . . . . . . . . . . . . . 72

3.4.3 Shapley supercluster . . . . . . . . . . . . . . . . . . . . . . . 73

3.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

4 Star formation in the Pisces-Cetus supercluster 76

4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

4.2 Star formation within Pisces-Cetus supercluster filaments . . . . . . . 77

4.2.1 Filament membership . . . . . . . . . . . . . . . . . . . . . . . 77

4.2.2 Star formation along the A2734-A2800 filament . . . . . . . . 80

Contents vii

4.2.3 Star formation properties of galaxies in all three filaments

combined . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

4.2.4 Star formation in high and low velocity dispersion clusters . . 84

4.2.5 Star formation in giant and dwarf galaxies . . . . . . . . . . . 87

4.2.6 Star formation in Groups . . . . . . . . . . . . . . . . . . . . . 88

4.2.7 Welch’s test results . . . . . . . . . . . . . . . . . . . . . . . . 91

4.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

4.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

5 Star formation in 2dFGRS filaments 98

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

5.2 The filament catalogue . . . . . . . . . . . . . . . . . . . . . . . . . . 99

5.3 The samples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99

5.3.1 Filament selection . . . . . . . . . . . . . . . . . . . . . . . . . 99

5.4 Star formation properties . . . . . . . . . . . . . . . . . . . . . . . . . 103

5.4.1 Properties of galaxies in the field . . . . . . . . . . . . . . . . 103

5.4.2 Star formation in galaxies belonging to filaments . . . . . . . . 104

5.4.3 Star formation in giant and dwarf galaxies . . . . . . . . . . . 107

5.4.4 Star formation in short and long filaments . . . . . . . . . . . 108

5.4.5 Star formation in groups . . . . . . . . . . . . . . . . . . . . . 108

5.4.6 Welch’s test results . . . . . . . . . . . . . . . . . . . . . . . . 110

5.5 Star formation in the PIM04 sample filaments . . . . . . . . . . . . . 112

5.5.1 Star formation within the filaments . . . . . . . . . . . . . . . 113

5.5.2 Star formation within giants and dwarfs . . . . . . . . . . . . 114

5.5.3 Star formation in groups . . . . . . . . . . . . . . . . . . . . . 115

5.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

6 Star formation in the Shapley supercluster 123

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

6.2 Spectroscopic data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

6.2.1 Removal of AGN . . . . . . . . . . . . . . . . . . . . . . . . . 127

6.2.2 Stellar absorption . . . . . . . . . . . . . . . . . . . . . . . . . 129

Contents viii

6.2.3 Flux calculations . . . . . . . . . . . . . . . . . . . . . . . . . 130

6.2.4 Dust attenuation . . . . . . . . . . . . . . . . . . . . . . . . . 131

6.2.5 Aperture correction . . . . . . . . . . . . . . . . . . . . . . . . 132

6.2.6 SFR calculation . . . . . . . . . . . . . . . . . . . . . . . . . . 132

6.3 Samples of galaxies in various environments . . . . . . . . . . . . . . 133

6.4 SFR as a function of distance from a cluster . . . . . . . . . . . . . . 136

6.5 Fraction of starburst galaxies . . . . . . . . . . . . . . . . . . . . . . 137

6.6 Fraction of passive galaxies . . . . . . . . . . . . . . . . . . . . . . . . 137

6.7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

7 Conclusions 141

7.1 Summary of main results . . . . . . . . . . . . . . . . . . . . . . . . . 141

7.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

Bibliography 145

A Optical Surface brightness fits to clusters (P-C) 160

B Optical Surface brightness fits to clusters (H-R) 163

C Optical Surface brightness fits to clusters (S) 168

D X-ray analysis of the Pisces-Cetus supercluster 172

D.1 X-Ray observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172

D.1.1 ROSAT archival pointed observations . . . . . . . . . . . . . . 172

D.1.2 Rosat all-sky Survey and Einstein IPC observations . . . . . . 173

D.1.3 The LX–σ relation . . . . . . . . . . . . . . . . . . . . . . . . 173

D.1.4 Pisces-Cetus supercluster results . . . . . . . . . . . . . . . . . 175

E The 2dFGRS “clean sample” of filaments 178

List of Figures

1.1 The power spectrum of density perturbations as a function of scale

size. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.2 The distribution of dark matter in the millennium simulation. . . . . 12

1.3 The galaxy redshift distribution for the 2dFGRS survey. . . . . . . . 15

2.1 The principle components used in generating the 2dFGRS η parameter. 35

2.2 Distribution η versus galaxy morphology. . . . . . . . . . . . . . . . . 36

2.3 Correlation between η and the equivalent width of the Hα emission

line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.4 Distribution of η versus the birth rate. . . . . . . . . . . . . . . . . . 38

2.5 A histogram of the η for 2dFGRS galaxies with z < 0.1 . . . . . . . . 39

2.6 Composite fit to the η distribution. . . . . . . . . . . . . . . . . . . . 40

2.7 Individual fits to the η distribution. . . . . . . . . . . . . . . . . . . . 40

3.1 Pisces-Cetus supercluster, clusters of galaxies with minimal spanning

tree links. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.2 Pisces-Cetus supercluster 2dFGRS and SDSS galaxies . . . . . . . . . 46

3.3 Pisces-Cetus supercluster, SuperCOSMOS galaxies. . . . . . . . . . . 47

3.4 Pisces-Cetus SuperCOSMOS galaxy Density contours . . . . . . . . . 48

3.5 Pisces-Cetus supercluster, clusters of galaxies in R.A.-redshift space . 48

3.6 Pisces-Cetus supercluster wedge diagram of 2dFGRS galaxies. . . . . 49

3.7 Pisces-Cetus supercluster, clusters of galaxies in Dec.-redshift space . 49

3.8 Horologium-Reticulum supercluster, clusters of galaxies with minimal

spanning tree links. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.9 Horologium-Reticulum supercluster ZCAT galaxies. . . . . . . . . . . 51

ix

List of Figures x

3.10 Horologium-Reticulum supercluster, clusters of galaxies in R.A.-redshift

space. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.11 Horologium-Reticulum supercluster Wedge plot of ZCAT galaxies. . . 52

3.12 Shapley supercluster, clusters of galaxies with minimal spanning tree

links. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

3.13 Shapley supercluster NED galaxies. . . . . . . . . . . . . . . . . . . . 53

3.14 Shapley supercluster, clusters of galaxies in R.A.-redshift space . . . . 54

3.15 Pisces-Cetus supercluster, galaxy cluster colour magnitude relation. . 60

3.16 Pisces-Cetus supercluster galaxy cluster radial velocity histograms. . 65

3.17 Horologium-Reticulum supercluster galaxy cluster radial velocity his-

tograms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

3.18 Shapley supercluster galaxy cluster radial velocity histograms 1. . . . 67

3.19 Shapley supercluster galaxy cluster radial velocity histograms 2. . . . 68

4.1 Pisces-Cetus 2dFGRS supercluster galaxies. . . . . . . . . . . . . . . 78

4.2 Pisces-Cetus supercluster, clusters of galaxies in the 2dFGRS region. 78

4.3 Three filaments of galaxies in the Pisces-Cetus supercluster. . . . . . 79

4.4 2dFGRS galaxies for the galaxy cluster Abell 2734 . . . . . . . . . . . 80

4.5 Mean η as a function of the distance from Abell 2734. . . . . . . . . . 81

4.6 Star forming and passive galaxy distribution for Abell 2800. . . . . . 82

4.7 Star forming and passive galaxy distribution for Abell 2734. . . . . . 83

4.8 Mean η as function of the distance from the nearest cluster. . . . . . 84

4.9 Histograms of η in each distance bin. . . . . . . . . . . . . . . . . . . 85

4.10 Mean η as a function of the distance from the nearest low or high σ

cluster. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

4.11 Mean η in giant or dwarf galaxies as function of distance from the

nearest cluster. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

4.12 Spatial distribution of giant and dwarf filament galaxies. . . . . . . . 88

4.13 Mean η of group or non-group galaxies as a function of distance from

the nearest cluster . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

4.14 Mean η of filament or field group galaxies as a function of distance

from the nearest cluster . . . . . . . . . . . . . . . . . . . . . . . . . 90

List of Figures xi

4.15 Histograms of richness and velocity dispersion for group galaxy samples. 91

5.1 Mean η as function of distance from the nearest cluster for the entire

2dFGRS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

5.2 Mean η as function of distance from the nearest cluster. . . . . . . . . 105

5.3 Histograms of η in each of the 8 distance bins. . . . . . . . . . . . . . 106

5.4 Mean η of giant or dwarf galaxies as a function of distance from the

nearest cluster. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

5.5 Mean η as function of distance from the nearest cluster for long and

short filaments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

5.6 Mean η of group or non-group galaxies as a function of distance from

the nearest cluster. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

5.7 Mean η of filament and field group galaxies as a function of distance

from the nearest cluster. . . . . . . . . . . . . . . . . . . . . . . . . . 112

5.8 Histograms of richness and velocity dispersion for group galaxy samples.113

5.9 Mean η as function of distance from the nearest cluster (PIM04a). . . 115

5.10 Mean η as function of distance from the nearest cluster (PIM04b). . . 116

5.11 Histograms of η within each distance bin. . . . . . . . . . . . . . . . . 117

5.12 Mean η in giant or dwarf galaxies as function of distance from the

nearest cluster. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

5.13 Mean η in group and non-group galaxies as a function of distance

from nearest cluster. . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

5.14 Mean η in filament and field group galaxies as a function of distance

from nearest cluster. . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

6.1 Example spectra of a 6dF starburst galaxy. . . . . . . . . . . . . . . . 126

6.2 Example spectra of a 6dF passive galaxy. . . . . . . . . . . . . . . . . 126

6.3 Example spectra of a 6dF AGN galaxy. . . . . . . . . . . . . . . . . . 127

6.4 BPT diagram of Shapley region galaxies. . . . . . . . . . . . . . . . . 129

6.5 Histogram of the uncalibrated SFR of galaxies in the Shapley region 1.134

6.6 Histogram of the uncalibrated SFR of galaxies in the Shapley region 2.135

List of Figures xii

6.7 Mean uncalibrated star formation rate as a function of distance from

the nearest cluster. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

6.8 Fraction of starburst galaxies as a function of distance from a cluster 138

6.9 Fraction of passive galaxies as a function of distance from a cluster. . 139

A.1 Surface brightness profiles for A0014, A0027 and A0074. . . . . . . . 160





A.6 Surface brightness profiles for A2800, A2824, and A4053. . . . . . . . 162

A.7 Surface brightness profiles for A2794, S1136 and S1155. . . . . . . . . 162

B.1 Surface brightness profiles of A2988, A3004 and A3009. . . . . . . . 163

B.2 Surface brightness profiles of A3074, A3078 and A3089. . . . . . . . . 164









B.11 Surface brightness profile of A3312 . . . . . . . . . . . . . . . . . . . 167

C.1 Surface brightness profiles of A1631, A1644 and A1709. . . . . . . . . 168

C.2 Surface brightness profiles of A1736, A3528N and A3528S. . . . . . . 169







List of Figures xiii

C.9 Surface brightness profiles of SC1327 and SC1329. . . . . . . . . . . . 171

D.1 (Top row) X-ray contours from pointed ROSAT PSPC observations,

superposed on optical (Blue) DSS images of the clusters Abell 85,

Abell 133 and Abell 2734. (Middle row) Similar images of Abell 14

(RASS), Abell 74 & Abell 117 (Einstein IPC), Abell 151 (RASS), and

(Bottom row) of Abell 2716, Abell 2794, Abell 2800, and Abell S1136

(all RASS). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

D.2 The relationship between Lx and σ for Pisces-Cetus supercluster clus-

ters with available X-ray literature data. . . . . . . . . . . . . . . . . 176

E.1 Galaxy position, mean η and mean percentage of passive galaxies in

the 2dFGRS filament sample batch 1. . . . . . . . . . . . . . . . . . . 178


















the 2dFGRS filament sample batch 10. . . . . . . . . . . . . . . . . . 187

List of Figures xiv





List of Tables

3.1 Clusters belonging to the Pisces-Cetus Supercluster . . . . . . . . . . 57

3.2 Clusters belonging to the Horologium-Reticulum Supercluster . . . . 58

3.3 Clusters belonging to the Shapley Supercluster . . . . . . . . . . . . 59

4.1 Virial radii for Pisces-Cetus filament clusters . . . . . . . . . . . . . 83

4.2 Welch’s test results for Pisces-Cetus filaments . . . . . . . . . . . . . 92

5.1 Filament type classification in the PIM04 sample . . . . . . . . . . . 100

5.2 Filament information for the 52 visually selected sample. . . . . . . . 101

5.3 Welch’s test results for “clean sample” filaments . . . . . . . . . . . 112

xv

Chapter 1

Captain James Cook: “I had ambition not only to go farther than any man had ever

been before, but as far as it was possible for a man to go.”

Introduction

Throughout history humans have become more and more aware of the universe in

which they live. Boundaries have moved beyond the hunting grounds of ancient

times, expanded beyond the horizon by explorers who dared to go where “here be

dragons” marked the map. Today we have gone beyond the bounds of our little

blue planet and out into the depths of space. Our vision has advanced out beyond

our solar system, out through the billions of stars of the Milky Way, to gaze upon

Andromeda and the other galaxies that form the local group. Then even further we

are drawn out into a universe of other groups of galaxies, huge clusters of galaxies

and a massive network of filaments linking them all together. Finally we arrive at

superclusters of galaxies. These are massive chains of clusters of galaxies linked by

filaments of galaxy groups and individual galaxies.

The term supercluster has been used to denote various entities in literature (see

§ 1.3). However, in this thesis we define the term to denote Large-scale structures

that are much larger than the virial radii of individual rich clusters (>∼10 h−170 Mpc).

Observations and simulations of the large-scale structure of the Universe have

revealed the presence of a network of filaments and voids in which most galaxies

seem to be found (Zucca et al., 1993; Einasto et al., 1994; Jenkins et al., 1998). This

implies that that the Universe is not homogeneous on scales below ∼ 100 h−170 Mpc

(Bharadwaj, Bhavsar, & Sheth, 2004; Shandarin, Sheth, & Sahni, 2004), which is the

scale of the largest common structures of galaxies, though the discovery of structures

1

1.1. Structure formation 2

far larger than these have been claimed (e.g., Brand et al., 2003; Miller et al., 2004).

Perturbations on the scale of superclusters are likely to still be in a linear growth

regime and have not yet reached equilibrium, or to have only recently left the linear

growth regime. If this is the case they have yet to condense out of the Hubble

expansion and can be analytically tractable containing valuable information about

the processes that occurred during their formation. Superclusters are an essential

tool to study the largest-scale density perturbations that have given rise to structure

in the Universe (e.g., Bahcall, 2000). They can be useful in quantifying the the

high-end mass function of collapsing systems and ratio of mass to light on the

largest scales, thus being useful in discriminating between dark matter and structure

formation models (e.g., Kolokotronis, Basilakos, & Plionis, 2002; Bahcall, 1988).

1.1 Structure formation

When the universe was much younger than it is now it was smoother and denser.

Superposed on this smooth background were small fluctuations in the density of

matter and the temperature of the Cosmic Microwave Background (CMB). Accord-

ing to the most popular current theory, initial Gaussian density perturbations in

the primordial universe lead to the formation of structure on different scales as the

universe expanded. The linear theory of gravitational instability shows that density

perturbations grow at best in proportion to the expansion factor of the universe. As

the universe has expanded by a factor of approximately 1000 since the decoupling of

radiation and matter at recombination, density perturbations can only have grown

by a factor of about 1000 since this time. Therefore, the fluctuations should be de-

tectable as small-scale anisotropies in the cosmic microwave background radiation.

This is indeed the case and such anisotropies have been observed by COBE (Smoot

et al., 1992) and more recently the Wilkinson Microwave Anisotropy Probe, WMAP

(Bennett et al., 1997), which used differential microwave radiometers to measure

temperature differences between two points on the sky.


1.1.1 The power spectrum

The cosmological density perturbations or matter overdensities are specified by the

quantity:

δ(x) =ρ(x) − 〈ρ〉

〈ρ〉 , (1.1)

where 〈ρ〉 is the mean density of the universe and ρ(x) is the mass density at position

x.

These spherically overdense regions in the otherwise uniform density universe

will start off decreasing in density at almost the same rate as the rest of the uni-

verse, following linear theory. However, the density gradually stops decreasing and

then starts to increase radically when a critical density is reached. For δ(x) ≪ 1,

the region is in the linear regime and it is possible to analytically model the collapse.

However, for δ(x) & 1 the collapse is in the non-linear regime and becomes too com-

plicated to model analytically and numerical simulations are needed. Superclusters

have been shown to have overdensities of the order of 2 or 3 (e.g., Fabian, 1991;

Fleenor et al., 2005) over scales of larger than 20 h−170 Mpc and will therefore have

only recently have left the linear regime.

Fluctuations in the CMB

The fluctuations in the smooth background must have been created by some kind

of mechanism. The only mechanism which fits with todays observations is inflation,

which refers to a period of exponential expansion of the universe which occurred

soon after the Big Bang (e.g., Albrecht et al., 1982). This process solves two major

problems, that of the flatness problem and the horizon problem. The rapid inflation

of the universe would have smoothed out spacetime allowing the flat universe we see

today. At the same time it explains how regions that are on opposite sides of the

universe today could once have been close enough to have been in communication

allowing for their almost identical CMB conditions. It also allows for seed fluctua-

tions for galaxy formation to have originated from quantum fluctuations that were


then inflated to a macroscopic scale.

1.1.2 The growth of perturbations

The initial Gaussian density perturbations are assumed to have a power-law spec-

trum,

Pi(k) = Akn, (1.2)

where n is the spectral index and k = 2π/L, where L is the size of the perturbation.

Zel’Dovich (1970) approximated the perturbations to be scale invariant or grow

at the same rate as the universe. This led to the Harrison-Zeldovich spectrum, with

n = 1,

P (k) ∝ k. (1.3)

Recent observations by WMAP, have shown the actual value of n in a flat Λ dom-

inated universe, to be remarkably close to the Harrison-Zeldovich approximation

with a value of 0.99 ± 0.04 (Spergel et al., 2003).

The power spectrum at any given time depends on this initial power spectrum

and the transfer function which describes how the initial power spectrum is mod-

ified over time by the physical processes present in the universe. Thus the power

spectrum at a given time in its dimensionless form is described by,

∆2(k) = kn+3 T 2(k, t), (1.4)

where T (k, t) is the transfer function. The amplitude of the perturbations will

continue to grow with time with the shape of the initial spectrum being maintained

in the linear regime. When δ approaches unity on a scale of size L the region

collapses and becomes non-linear, where ρ = ρ0(1 + δ), ρ being the density of the

region and ρ0 the mean density of the universe.

1.2. Dark matter and cosmological models 5

The Press-Schechter formalism

As mentioned above, the non-linear phases of collapse of the matter are too com-

plex to allow completely analytic solutions. Press & Schechter (1974) created a

simplified analytic approach where structure has formed hierarchically from initial

Gaussian fluctuations. They adopted initially overdense regions that would expand

at the same rate as the density of the rest of the universe until z approaches zvir,

the redshift at which the region starts to collapse and becomes virialised. At this

time the region will start to free fall until it collapses to a point. They formulate an

equation which tracks the evolution of the density across regions containing a mass

M on average. This results in an analytical solution where the form of the mass

distribution remains constant, even as the scale of the collapsing objects increases.

This is shown in Eq. 1.5 which defines the fraction of mass fg that is in virialised

structures exceeding mass M at a given redshift.

fg(M, z) = erfc

[

(1 + z)δc√2σ(M, 0)

]

, (1.5)

where erfc is a complementary error function, δc is the critical overdensity and σ is

the r.m.s mass fluctuation over the spherical region containing the mass M

1.2 Dark matter and cosmological models

It has now become obvious that that the luminous matter in the universe only makes

up a very small percentage of the mass in the universe. Observations as far back as

1933 (Zwicky, 1933) showed that the coma cluster had insufficient mass to explain

the velocity dispersion of the galaxies. Further evidence came in the form of the

rotation curves of galaxies. Rubin & Ford (1970) showed that rather than rising to

a peak velocity then dropping as predicted the rotation curve of Andromeda was

in fact flat out to large radii. This has been confirmed for many other galaxies

of varying morphology. More recently X-ray derived masses of clusters of galaxies

and those from gravitational lensing have confirmed the presence of an excess of

mass over that which can be explained from optical observations. The additional


missing mass is referred to as dark matter. Dark matter plays an important role in

the formation of structure as its gravitational influence dominates that of the other

components for most of the life of the universe. It is therefore essential to understand

the properties, amount and distribution of dark matter before large scale structure

can be explained. Dark matter is the dominant influence on the form that the

transfer function and hence the power spectrum described by Eq. 1.4 takes.

A possible candidate for dark matter is massive astrophysical compact halo ob-

jects (MACHOs) such as brown dwarfs and neutron stars. These like the luminous

matter in the universe are baryonic. However, due to constraints on the contri-

bution of baryons to the critical density Ωb imposed by Big Bang Nucleosynthe-

sis (e.g., Burles, Nollett, & Turner, 2001) only a small fraction can be baryonic

(Ωbh2 = 0.020 ± 0.002). Therefore, models were proposed that incorporated non-

baryonic matter in structure formation.

Each of the model types results in a unique form of the power spectrum which

in turn, if correct should describe the universe that we observe today. Examples of

the forms taken by two possible models are shown in Fig. 1.1. The actual power

spectrum of the universe can be found by using the two point correlation function

of galaxies in large scale galaxy surveys, e.g., the APM Galaxy survey (Maddox et

al., 1990) and compared with dark matter models.

1.2.1 Hot Dark Matter

Hot dark matter (HDM) consists of particles that decouple when relativistic. These

particles have a number density roughly equal to that of the microwave background

photons. To remain relativistic for longer periods requires their masses to be less

than ≈ 100 eV. A major advantage of HDM is that it has a definite candidate

in the neutrino which had been suggested to oscillate from one species to another

and hence have non-zero mass (Fukuda et al., 1998). The major problem with

HDM is that in the early universe most of the matter density would have been due

to neutrinos. At this time their speeds would have been too great to be caught

in any overdense regions. Therefore, density fluctuations could only appear after

the universe had expanded enough to let the neutrinos cool and slow down. This


Figure 1.1: The power spectrum of density perturbations as a function of scale size for the

standard HDM and CDM models. (White, 2006). (§1.2)

means that the HDM model would have insufficient power on small scales, i.e., less

small scale structure than that observed (e.g., White, Frenk, & Davis, 1983; White,

Davis, & Frenk, 1984; Zeng & White, 1991). This can be seen in Fig. 1.1 where

the HDM peaks for values of approximately k = 0.1 which corresponds to scales of

L ∼ 10 h−1 Mpc. For scales smaller than 10 h−1 Mpc the HDM model rapidly loses

power and predicts no structures at scales of a few h−1 Mpc or less, excluding galaxy

size structures at the current epoch. The power spectrum changes over time, with

structures forming when a certain threshold of power is exceeded. It can be seen

that the first part of the HDM model to pass a threshold will be at its peak value,

at approximately k = 0.1 and so structures of approximately 10 Mpc will be formed

first. At all times there will be more large scale structure due to the gradual slope

towards low values of k, compared with the steep slope at higher values of k. Thus

HDM is a top down model with larger structures forming first.

Cold Dark Matter

Cold dark matter dominated universes (CDM) have been extensively modelled with

the use of N-body simulations and show a bottom-up structure formation (e.g.,

Peebles, 1982). The most likely candidates for non-baryonic CDM are Weakly in-


teracting massive particles (WIMPS) such as neutralinos, gravitinos, photinos and

higgsinos predicted by supersymmetric theories. Structure grows out of Gaussian

fluctuations with the scale invariant spectrum proposed by Harrison and Zeldovich

, see equation (1.3). The perturbations in the CDM begin to grow at the epoch of

matter-radiation equality but are unstable prior to decoupling. Only after recombi-

nation can the perturbations in the baryons begin to grow by falling into the CDM

potential wells. As material continues to flow into the density fluctuation, the fluc-

tuation continues to grow in size and accrete more matter. Galaxies are eventually

made by the coalescence of larger and larger clumps of matter, and later clusters

and superclusters of galaxies form as the gravitational clustering continues. Thus

the smallest structures are made first and a bottom up formation is observed. This

can be seen in Fig. 1.1 where the CDM model has no peak and the highest point

in the model is for high values of k. As the power spectrum evolves over time, this

point at high values of k will be the first to exceed the power threshold needed for

structure to form and so the smallest structures will form first. One of the greatest

successes of this model is its ability to produce structures with masses ranging from

small galaxies to those of rich clusters with simulations being indistinguishable from

surveys. This success is only possible though if the galaxies and the dark matter are

distributed differently (see §1.2.4). However, CDM does have its problems which

include an excess of faint galaxies at low luminosities and a lack of power on large

scales (> 10 h−1 Mpc), i.e. less large scale structure than is seen (Davis et al., 1992,

e.g.,). The lack of power can be seen in Fig. 1.1 where the power of the CDM model

has dropped by a factor of nearly 106 from that of scales of a few h−1 Mpc by the

time it reaches scales > 10 h−1 Mpc. The lack of power can be solved in three main

ways:

1. Reducing the the mean mass density, thus reducing Ω which forms part of the

transfer equation. However, without another parameter in the universe the

value of Ω can’t be reduced and still be consistent with a flat universe and

CMB fluctuations. This can however, be solved with the introduction of Dark

Energy (see §1.2.3).

2. Tilting the initial power spectrum by changing the spectral index, n (Lidsey,


1994).

3. CDM and HDM to get warm dark matter (Colın, Avila-Reese, & Valenzuela,

2001)(see §1.2.2).

1.2.2 Warm Dark Matter

Warm dark matter (WDM), is a simple modification to the CDM model where the

dark matter particles have an initial kinetic energy. WDM particles have masses

of ∼ 1 keV compared to ∼ 1 GeV in CDM and ∼ 10 keV in HDM models. The

higher velocities than the CDM particles leads to a smoothing out of small-scale

fluctuations and hence the number of small haloes formed is suppressed reducing

the excess of small scale structures found in CDM. However WDM retains enough

of the CDM characteristics to allow for early structure formation on small scales.

However, achieving this balance on large and small scales puts stringent limits on

the mass of the various neutrino species.

1.2.3 Cold Dark Matter with Dark Energy

Data from sources such as cosmic microwave background (CMB) (e.g., Spergel et

al., 2003), measurements of the brightness of distant supernovae (e.g., Perlmutter

et al., 1999) and the abundance of present day of massive galaxy clusters (e.g.,

Bahcall & Fan, 1998) to name just a few are all suggesting a universe where matter

only makes up less than 30% of the critical density (ΩM < 0.3). A dark energy

component (ΩΛ < 0.3) accounts for the other 70% and maintains a flat cosmology.

Λ cold dark matter models ΛCDM are also most commonly considered in the scale

invariant spectrum of density perturbations proposed by Harrison and Zeldovich.

Some of the CDM is replaced with a cosmological constant Λ but a flat geometry

such that Ω = Ωm + ΩΛ = 1 is maintained. The latest values from WMAP finds

Ωmh2 = 0.14±0.02, Ωbh2 = 0.024±0.001 and h = 0.72±0.05 (Spergel et al., 2003).

Therefore, further models must be created to incorporate the new data. (Efstathiou,

Sutherland, & Maddox, 1990, e.g.,). A ΛCDM model due to its lower value of Ωm

is able to predict more large scale structure than the standard CDM model. With


the current best values from WMAP of Ωm = 0.27 and h = 0.72, structures of over

70 h−1 Mpc are possible, better recreating supercluster sized structure.

1.2.4 Bias

Bias is a measure of how well the observed large scale structure such as galaxies,

clusters and superclusters trace the underlying mass distribution from models. The

concept of bias was first introduced by Kaiser (1984) to explain the clustering prop-

erties of Abell clusters. An object of a certain mass will collapse at an early time

if it is a region of a peak in the initial density field. So galaxies forming in these

overdense regions will form sooner and hence there will be an enhanced abundance

of these galaxies. They will be more clustered and show increased bias. In the linear

regime, where density fluctuations are small the mass overdensity and the galaxy

overdensity can be related by the linear bias parameter b, where,

(

δρ

ρ

)

galaxies

= b

(

δρ

ρ

)

mass

. (1.6)

Hence, observations of clustering on large scales only allow us to determine the

mass fluctuations if we know the value of b. Lahav et al. (2002), using 2dF Galaxy

Redshift Survey (2dFGRS) and CMB data in a ΛCDM universe, find that optically

selected galaxies are almost unbiased, with b ∼ 0.96. However, Simon et al. (2004)

find that galaxies are less clustered than the total matter, and thus are anti-biased,

demonstrating that biasing is still an open subject.

1.2.5 Peculiar velocities

The high intensity activity in the study of the large scale motions in the universe

was launched by the finding of the “seven samurai” (Burstein et al., 1986) that the

Local Group participates in a large streaming motion. Under the assumption that

fluctuations are linear, the continuity equation, the Euler equation of motion and

the Poisson field equation can be used to to obtain the relation between density and

velocity, given by:


· υ = −Ω0.6m δm, (1.7)

where δm = (δρ/ρ)mass is the mass density contrast, υ is the peculiar velocity and

Ωm is the mass density parameter. This relation can be used to predict peculiar

velocity fields from the galaxy density fields of all-sky redshift surveys and this

can be compared with measured peculiar velocities. From these comparisons a

dimensionless quantity, β = Ω0.6m /b is obtained. The redshift surveys used now

usually result in regions of over 100 h−1 Mpc being studied. Such large regions

should still be in the linear regime and so the linear fluctuation assumptions are

valid. With the value of Ωm being tightly constrained by WMAP these studies can

give an estimate of the bias, b, over large scales. Radburn-Smith, Lucey, & Hudson

(2004) used the peculiar velocities of type 1a supernovae to obtain β = 0.55± 0.06,

while Hudson et al. (2004) obtain a lower value of β = 0.39 ± 0.17 from the study

of the streaming motions of Abell clusters.

1.2.6 N-body simulations

As mentioned earlier when a region leaves the linear regime it is no longer possible

to analytically predict its evolution and hence numerical simulations are needed.

The Virgo consortium used the Millennium simulation of over 1010 particles to trace

the evolution of the matter distribution in a ΛCDM universe (Springel, 2005). The

model used a ΛCDM model with Ωdm = 0.205, Ωb = 0.045, ΩΛ = 0.75, h =

0.73 and an initial spectral index of n = 1. This has resulted in a sufficient mass

resolution over volumes similar to those of the large redshift surveys (2dFGRS,

SDSS) to allow direct comparisons with observations. The simulation volume was a

box of 500 h−1 Mpc which resulted in the 10 billion particles, each having a mass of

8.6×108 h−1M⊙. This was enough for dwarf galaxies (L > 0.1L∗) to be represented

by approximately 100 particles, galaxies like the Milky way by approximately 1000

particles and rich clusters of galaxies several million particles.

1.3. The definition of a supercluster 12

Figure 1.2: The distribution of dark matter in a 15h−1 Mpc thick slice at a redshift of zero from

the millennium simulation. The intensity shows the surface density with the brightest regions

being the densest. The linear scale is shown by the bar. (§1.2.6)

1.3 The definition of a supercluster

The term supercluster has been used to describe structures from just a couple of clus-

ters separated by just a few h−170 Mpc (e.g., the A1367-Coma supercluster, Gavazzi

et al., 1998) up to structures larger than our ours (Brand et al., 2003), spanning

distances of 100 h−170 Mpc or more. In this thesis our superclusters are defined in

the supercluster catalogue of Raychaudhury et al. (2007). These superclusters have

been defined with the use of a minimal spanning tree (MST) algorithm with a max-

imum linking length of 20 h−1100 Mpc (i.e. no links between adjacent clusters on the

tree larger than 20 h−1100 Mpc are considered). This length is approximately where

the cluster-cluster correlation function becomes one, i.e. the length scale at which

there is no clustering above that of a random sample. Even on slightly larger scales,

say, at 25 h−1100 Mpc, the correlation function has the same value, but the detailed

structure of the supercluster changes. Raychaudhury et al. (2007) considers both 20

h−1100 Mpc and 25 h−1

100 Mpc as maximum linking length, and produces two different

catalogues. An example of this is the Pisces-Cetus supercluster which consists of

two unlinked parts of 5 and 11 clusters when a linking length of 20 h−1100 Mpc is used.

1.3. The definition of a supercluster 13

This however increases to one large supercluster of 19 members if the 25 h−1100 Mpc

links are used. The linking length of 25 h−1100 Mpc results in superclusters which have

a maximum size of the order 100 h−170 Mpc. It is therefore important to know at

which size superclusters become just a random collection of galaxies rather than a

statistically significant structure.

Pandey & Bharadwaj (2005) use SDSS data to find the maximum length of

filament which is statistically significant. They take a volume limited sample over

the redshift range 0.08 ≤ z ≤ 0.2, extinction corrected Petrosian r band apparent

magnitude 14.5 ≤ mr ≤ 17.5 and absolute magnitude range −22.6 ≤ Mr ≤ −21.6.

This results in 5315 galaxies distributed in two wedges, spanning 91 degrees (NGP)

and 65 degrees (SGP) in RA. and thickness 2 degrees.

They use a technique where the 2D galaxy distribution is embedded in a 1

h−1100 Mpc by 1 h−1

100 Mpc rectangular grid. Grid cells having a galaxy within them

are termed as filled (assigned a value of 1) and those without a galaxy present are

termed as empty (assigned a value of 0). The filamentarity of a cluster is defined

based on a single 2D “shapefinder” statistic (Bharadwaj et al., 2000), where a value

of 1 is a filament, a value of 0 is a square and the values change from 0 to 1 as

a square is deformed into a filament. They then use a statistical technique called

shuffle to determine the largest scale length at which the filamentarity is significant.

The shuffle technique involves taking squares with sides of length L. These

squares are then randomly interchanged, thus destroying structures larger than L

but maintaining those smaller than L. For a fixed value of L, if the shuffled data

has an average filamentarity lower than the initial data then the original data had

more filaments with length longer than L. They calculate the difference in the fil-

amentarity of the shuffled and original cluster data (χ2 per degree of freedom) at

each value of L. They find that shuffling the data with L>90 h−1100 Mpc does not

result in a significant difference in the filamentarity of the two samples. Therefore,

the longest filament which is statistically significant is 80 h−1100 Mpc, or 114 h−1

70 Mpc.

Therefore, our superclusters which have a maximum size of the order 100 h−170 Mpc,

should therefore be statistically significant.

1.4. Observational Surveys 14

1.4 Observational Surveys

1.4.1 The Two Degree Galaxy Redshift Survey

The Two degree Galaxy Redshift Survey (2dFGRS) is a large spectroscopic survey

in the southern celestial hemisphere covering approximately 1500 square degrees.

Spectra for 245,591 galaxies were obtained in three regions, the North Galactic pole

region , South Galactic pole region and a series of random fields. This makes it the

second largest redshift survey to date, coming above the VIRMOS galaxy redshift

survey (Le Fevre et al., 2004) of approximately 150000 galaxies but falling below the

Sloan Survey which is discussed later in this section. The survey is performed with

the Two-degree Field multifibre spectrograph on the Anglo-Australian telescope,

capable of observing up to 400 objects at once within the two degree field. The

survey is based on an extended version of the Automated Plate Measuring catalogue

of over 5 million objects.

The overall incompleteness of the source catalogue varying with apparent mag-

nitude is 10− 15%, the incompleteness being due to effects such as merged images,

misclassification of some galaxies as stars and the misclassification of some low sur-

face brightness galaxies as noise. The survey magnitude limit varies across the survey

regions and is detailed in the survey magnitude mask. Initially before improvements

to the photometric calibrations target galaxies were limited to extinction corrected

magnitudes of bJ > 19.45. The 2dFGRS is the first survey to be large enough to

study effects over scales of larger than 100 h−1 Mpc. One such effect that has been

studied is the Kaiser effect (Kaiser, 1987), which studies the gravitational collapse of

cosmological structures. In the collapsing regions there should exist coherent infall

velocities of galaxies which will cause an apparent flattening of structures along the

line of sight. Peacock et al. (2001) used the galaxy two-point correlation function

to show that the Kasier effect is observed for these large scales and combined with

CMB data their results are consistent with a Ωm = 0.3 universe. Other results have

included calculating the galaxy power spectrum (Percival et al., 2001), the luminos-

ity dependence of galaxy clustering (Norberg et al., 2001) and the environmental

effects on star formation rates near clusters (Lewis et al., 2002) to name just a few.


Figure 1.3: Map of the galaxy redshift distribution for the completed 2dFGRS survey. .Taken

from Colless et al. (2003). (§1.4.1)

1.4.2 The 2dFGRS Percolation-Inferred Galaxy Group cat-

alogue

The 2dFGRS Percolation-Inferred Galaxy Group (2PIGG) catalogue is a catalogue

of groups based on the North and South strips of the 2dFGRS catalogue consisting

of approximately 220,000 galaxies (Eke et al., 2004). They chose a friend-of-friends

algorithm to find the groups. These algorithms link together all the galaxies within

a certain linking distance of the centre of each galaxy. So that the groups all have a

similar overdensity throughout the sample, this linking length was varied with red-

shift to counter the reduced number density of galaxies detected at larger redshifts.

The linking length should ideally be scaled in the perpendicular direction (plane

of the sky) and the parallel (line of sight) directions such that a group sampled at

different completeness should have its edges in approximately the same position.

However, care has to be taken that the linking lengths do not become too large

compared to the size of gravitationally bound structures. The shape of the linking

volume was taken to be a cylinder to account for elongation in the redshift direction,

and to best recover groups that trace the underlying dark matter halo.

Eke et al. (2004) also showed that the overdensity enclosed in the group was

dependent on the mass of the underlying halo. This can result in a systematic


bias in the projected size and velocity dispersion, resulting in small groups with

overestimated sizes or large clusters with underestimated sizes. To correct for this

they estimated the halo mass in which each galaxy is found. This was done by

measuring the galaxy density relative to the background, and then using this density

contrast to scale the size and aspect ratio of the linking cylinder. The size of the

linking volume is thus dependent on the maximum size of the perpendicular linking

length (L⊥) , the aspect ratio of the linking cylinder (Rgal) and the number of mean

intergalaxy separations defining the perpendicular linking length (bgal). These values

are in physical coordinates and set at optimum values while the parameters in co-

moving space vary with redshift and galaxy density.

Optimum values were found by comparing groups found from a mock 2dFGRS

catalogue with their parent dark matter halos. The 220,000 galaxies in the initial

sample were reduced to 191,000 after all galaxies within fields with less than 70%

completeness, and in all sectors (overlapping field areas) with completeness less than

50%, were removed. Weights were then applied to these galaxies by assigning all the

galaxies in the parent APM catalogues with no recorded redshift to the nearest 10

members with redshifts. The co-moving number density of galaxies was calculated

at each angular position and redshift. This mean observed galaxy density for each

galaxy was then used with the friend-of-friends algorithm with optimum values of

L⊥ = 2 h−1 Mpc, Rgal = 11 and bgal = 0.13 to find real groups in the 190,000

galaxy sample. This resulted in 55 % of galaxies being part of groups of at least two

members. 28,877 groups were found with at least 2 members and 7,020 groups with

at least 4 members.

1.4.3 The Six degree Galaxy Survey

Since 2001 the Six degree Galaxy Survey (6dFGS) has obtained over 120,000 red-

shifts in the southern sky. The final release is due in late 2006, by which time the

survey will have covered an area 8 times larger than that of the 2dFGRS. The sur-

vey is performed with the six-degree field multi-object fibre spectroscopy system on

the UK Schmidt telescope at the Anglo-Australian Observatory (6dF). The 6dF is

capable of taking 150 simultaneous spectra in a field of a 5.7 degree diameter. The


primary sample for the survey is extracted from the near infrared (NIR) two micron

all sky survey (2MASS)(Jarrett et al., 2000). The use of a NIR survey means that

the bias towards currently star forming galaxies, found in the SDSS and 2dFGRS,

would be minimalised. Each field takes approximately 1.5 hours and repositioning of

fibres and other overheads take about 40 minutes, resulting in 5 fields being observed

a night on average.

1.4.4 The Sloan Digital Sky Survey

Funded by the Alfred P. Sloan Foundation, the Sloan Digital Sky Survey (SDSS) is

the largest redshift survey to date and is still growing. The fifth data release con-

tained spectra for approximately 675,000 galaxies and 79,000 quasars with the aim

being to get over 1 million galaxies by the end of the survey. Imaging is carried out

in drift scan mode using a wide-field 2.5 m telescope at Apache Point Observatory,

New Mexico. Photometry is gathered in five broad bands, (u,g,r,i,z) in the range

from 3000 to 10,000 A. Each plate can accommodate 640 fibres, about 50 of which

are reserved for calibration targets, which leaves approximately 590 fibres for tar-

gets. Plates are exposed in a series of 15 minute sessions after which signal-to-noise

ratio (S/N) diagnostics are performed. The 15 minute exposures are continued until

until the cumulative median (S/N)2 > 15 at g* = 20.2 and i* = 19.9 in each of

the 4 CCD detectors (One red and one blue in each of the two spectrographs). The

nominal exposure time is 45 minutes. The spectroscopic survey aims to observe a

complete sample of galaxies, selected to be brighter than r* = 17.77, using Petrosian

magnitudes 1. Like the 2dFGRS the SDSS has been used extensively to investigate

the large scale structure of the universe. Studies have included, the clustering prop-

erties of galaxy clusters (Basilakos & Plionis, 2004), constraining the amplitude of

the matter power spectrum (Viana, Nichol, & Liddle, 2002) and large scale galaxy

1Galaxies do not all have the same radial surface brightness profile, and have no sharp edges,

Therefore, a method is needed to measure a constant fraction of the total light, independent of

the position and distance of the object. The SDSS has adopted a modified form of the Petrosian

(1976) system, measuring galaxy fluxes within a circular aperture whose radius is defined by the

shape of the azimuthally averaged light profile.

1.5. Cosmology in this thesis 18

clustering (Gaztanaga, 2002), to name just a few.

1.4.5 Super COSMOS

SuperCOSMOS is a machine used to digitise Sky Survey plates taken with the UK

Schmidt telescope, the ESO Schmidt, and the Palomar Schmidt telescopes. The

photographic plates are digitised to 15 bits with a resolution of 10 microns. The

resulting database is approximately 2.5 terabytes in size and contains 3.7 billion

individual object detections. The database covers the southern sky (dec < +3.0)

in three wavebands (BRI), with the R band represented at two epochs. Initially the

source pairing was done “on-the-fly” but a more detailed analysis of merged objects

is performed in the SuperCOSMOS Science Archive (SSA). Each scanned plate in

the SSA results in a pixel map. This map is then processed using Image Analysis

Mode, or IAM, software to produce a list of parameterised detections on each plate.

The “on-the-fly” method uses a series of pair index pointers between any two given

plate datasets, however this can result in the same slave detection being paired with

more than one master image. The SSA uses the same pair indices but removes any

multiple pairings based on absolute proximity, i.e. the nearest slave is chosen.

1.5 Cosmology in this thesis

Throughout this thesis the cosmology used is ΩM = 1 and H0 =70 km s−1 Mpc−1,

though the trends we present do not crucially depend on these parameters. It can

be shown that for the Shapley supercluster, for example, a dark energy dominated

cosmology ΩΛ = 0.7, Ωm = 0.3, at the mean redshift of z = 0.0476 would be at a

distance of 211h−170 Mpc compared with 206 h−1

70 Mpc for our ΩM = 1 cosmology.

This amounts to a 2.5 % difference in the distances, which is within the error budget

of most of the calculations we perform.

1.6. Thesis Outline 19

1.6 Thesis Outline

In Chapter 2 we give a brief introduction into star formation in galaxies, covering

areas such as trends with time and environment, star formation indicators and a

summary of the 2dFGRS star formation parameter η. Chapter 3 investigates the

Pisces-Cetus, Horologium-Reticulum and Shapley superclusters, looking at their

spatial structure and obtaining estimates of their minimum mass and consequently

their mass overdensities. The star formation properties of the Pisces-Cetus super-

cluster are looked at in Chapter 4 using the η parameter. The dependency of star

formation on its environment is investigated in a range of areas including within

clusters and groups, within the supercluster and in the field, in dwarf and giant

galaxies and around low and high velocity dispersion clusters. Chapter 5 looks at

some of the same star formation environmental relations in much larger samples of

filaments of galaxies using the same η parameter. Star formation is also investi-

gated in Chapter 6, but this time 6dF equivalent widths are used to estimate star

formation within the Shapley supercluster region. Our findings are summarised in

Chapter 7 and future work discussed.

Chapter 2

Lady Astor: “Winston, if I were your wife I’d put poison in your coffee.”

Sir Winston Churchill: “Nancy, if I were your husband I’d drink it.”

Star formation in galaxies

2.1 Star formation as a function of time

It is generally accepted that the stellar populations in galaxies in the cores of clus-

ters are predominantly old. Most of the galaxies have early type morphology with

suppressed star formation, with the bulk of stars forming at z > 2. The tight cor-

relation of colour magnitude relations support this, as recent star formation would

result in a much greater scatter than that observed (Bower, Lucey, & Ellis, 1992;

Gladders et al., 1998). Other relations such as that between the Mg2 line strength

(metallicity indicator) and central velocity dispersion (e.g. Guzman et al., 1992) or

that in the fundamental plane of early type galaxies (e.g. Fritz & Ziegler, 2003) also

show little scatter.

With little star formation at the current epoch it is sensible to assume that as

you go back in time you will reach a period where the relations break down and

star formation is more prevalent. van Dokkum & Stanford (2003) have shown that

the fundamental plane relation remains tight at z = 1.27, but there is little or

no evidence for tight relations beyond z = 2. However, studying only the early

type galaxies or any subset of the total cluster population can result in biases. An

example of this is the “progenitor bias” described by van Dokkum & Franx (2001),

where by the progenitors of the youngest present day early type galaxies drop out

of the sample at high redshift. i.e. a significant fraction of present-day, early-type

20

2.1. Star formation as a function of time 21

galaxies was transformed from star-forming galaxies at z < 1 and so for z > 1,

galaxies which are early-type now may not be included in the sample.

The star formation rate (SFR) in cluster cores has also been studied as a function

of redshift. This has been extensively performed on the basis of colours. Butcher

& Oemler (1984) showed that clusters show a larger proportion of bluer (higher

temperature and higher SFR) galaxies at progressively higher redshifts. This ef-

fect has become known as the “Butcher-Oemler effect” and has been confirmed by

more recent studies (Margoniner et al., 2001). This has helped establish clusters as

evolving systems where star formation and galaxy morphology are dependent on the

environment. However, once again care has to be taken to consider possible biases.

The magnitude limit can be a potential bias where by blue galaxies will fade by up

to a magnitude when star formation ends and thus are not directly comparable to

the red galaxies. Another potential bias can come from the contamination of cluster

members by field galaxies due to projection effects. At low redshifts this effect may

be minimal, but at larger redshifts, with their bluer field populations, this effect will

be greater. De Propris et al. (2004) have concluded that the observed changes in the

blue fraction are dependent on the luminosity limit, cluster-centric radius and more

generally the local galaxy density but not the properties of the individual clusters.

Poggianti et al. (2006) also confirm the “Butcher-Oemler effect” but also show that

the morphology of galaxies change to later-type toward higher redshifts. Thus, there

is also a morphological version of the “Butcher-Oemler effect”.

The fraction of star forming galaxies as a function of redshift can also be studied

spectroscopically. Poggianti et al. (2006) use the Equivalent Width (EW) of the [OII]

line as an indicator of ongoing star formation in a high (z=0.4–0.8) and low (z=0.04–

0.08) redshift galaxy sample to find the fraction of passive galaxies. They propose a

scenario in which the passive galaxies consist of two populations, primordial which

had all their star formation at z > 2.5 and quenched galaxies where the SFR had

been reduced due to dense environments at later times. The Millennium simulation

is used to show that their observed relations between the fraction of passive galaxies

and velocity dispersion at high redshifts is consistent with that of galaxies that were

in groups at z = 2.5, with primarily a primordial passive population. The high

2.2. Star formation as a function of environment 22

redshift sample is found to be consistent with galaxies that have been in clusters

over the last 3 Gyr, with 60% quenched galaxies. This would mean that galaxy star

formation histories of galaxies are closely linked with the environment, even at high

redshift..

2.2 Star formation as a function of environment

Early works have also shown that the relative morphological content of galaxies in

a given volume of space is dependent on the local projected galaxy density, with

more elliptical galaxies and less spirals at higher densities (e.g. Dressler, 1980).

Menanteau et al. (2006) have shown that the SFR is dependent on the morphology of

the galaxy with spiral galaxies being the main provider to the star formation density

at all redshifts. However, Ravindranath et al. (2006) use high redshift Lyman-break

galaxies 2.5 < z < 5 to show that at higher redshifts many star forming galaxies

have elongated structures. Thus at higher redshifts a significant fraction of star

formation may be occurring in galaxies which are comprised of gas rich filaments.

Therefore, morphological type can not always be used as a proxy for SFR.

The effect of the density of the environment has been studied extensively in

clusters of galaxies, where a large range of projected surface density can be probed.

There is clear evidence that SFRs are highly suppressed in galaxies within the cores

of rich clusters (Dressler, 1980). Furthermore, the current SFR is shown to increase

with decreasing density and increasing distance from a cluster core. Balogh et al.

(1999) were one of the first to study the SFR away from cluster cores. They found

a strong radial dependence on SFR and that the SFR had not yet reached the field

value as far out as the virial radius. The arrival of the 2dFGRS and SDSS has

allowed much more accurate work to be done with the detailed redshift information

removing contamination from interlopers. From these surveys, Lewis et al. (2002)

and Gomez et al. (2003) have shown a correlation between the median SFR and

the local density. There is a sharp transition in the correlation at approximately 1

galaxy per h−2 Mpc−2. Beyond 1 galaxy per h−2 Mpc−2 the median SFR has values

very similar to the field values but below 1 galaxy per h−2 Mpc−2 the median SFR

2.3. Star formation indicators 23

begins to drop rapidly.

The SFR in clusters away from the core does not reach that of the field until

beyond 3 h−1Mpc (∼2 times the virial radius) from the centre of the clusters. This

shows that ram pressure stripping can’t be the only process that is suppressing the

SFR as this is only present in the most dense environments. They also conclude

that the SFR dependence on density is independent of the velocity dispersion of

the cluster and hence the SFR is independent of the large scale structure of the

environment (group or cluster). However, while Balogh et al. (2004) also find that

the correlation is independent of velocity dispersion, they suggest that fewer galaxies

in supercluster like environments have significant Hα emission and that there may

be some correlation at lower densities on scales > 5 h−1 Mpc.

Haines et al. (2006a) compare the environmental dependence of giant (MR <

−20) and dwarf galaxies. They find that the SFR in giant galaxies are in agreement

with the above studies with SFR approaching field values at 3–4 virial radii. How-

ever, the dwarf galaxies show a sharp transition at approximately the virial radius

from predominantly passive to predominantly star forming. This means that dwarf

galaxies may preferentially lose their gas reserves and hence become passive when

they encounter effects such as ram pressure striping or galaxy harassment.

2.3 Star formation indicators

2.3.1 Recombination lines of Hydrogen

High temperature OB stars cause the ionisation of the HII nebular gas that sur-

rounds them. The hydrogen electrons ionised by Lyman continuum photons with

energies above 13.6 eV, recombine with the atoms. The initially excited atom jumps

down to less excited states, and, in doing so, releases energy at specific wavelengths,

which is seen as emission lines in the spectrum. For a radiation bounded system, the

flux of the hydrogen recombination lines scales directly with the flux of the ionising

radiation from the stars. The strongest emission line is the Lyman Hα , the strength

of which can be determined by taking the equivalent width. Equivalent Width is

defined as the rectangular section of a surface counted between the level of the con-


tinuum, normalised to unity, and reference zero, having a surface area identical to

the profile of the line. The relation of Kennicutt (1998b),

SFR(IR) (M⊙yr−1) = 7.9 × 10−42LHα (erg s−1), (2.1)

where LHα is the total Hα luminosity, can be used to gain an estimate the SFR.

Because nearly half of the ionising atoms produce a Hα photon (Kennicutt et

al., 1998a) this technique is very sensitive. This combined with the direct coupling

between nebular emission and SFR and the ability of even small telescopes to obtain

high resolutions has enabled this technique to provide the most detailed information

on SFRs in galaxies.

However, the observed spectrum of the galaxy is a combination of the nebular

emission lines and the combined spectra of the constituent stellar population. There-

fore, the accurate measurement of the nebular emission lines relies on the removal of

the absorption lines in the underlying stellar spectrum. The stellar spectrum can be

recreated by either spectral synthesis or evolutionary synthesis models (e.g., Bruzual

& Charlot, 2003). Spectral synthesis creates the model spectrum by integrating the

spectra of star clusters spanning the range of types of star expected to be present

in the galaxy population. This is best used in elliptical galaxies and spiral bulges

where the population types are well constrained. In active star forming galaxies the

evolutionary synthesis is best used. These use a theoretical stellar evolution model,

coupled with models of stellar atmospheres and an assumed initial mass function to

create integrated spectra over a range of star formation histories. These are then

compared with the observed spectrum to find the stellar properties of the galaxy.

Extinction due to dust in the interstellar medium remains the main problem

with this technique. The extinction in normal galaxies can be estimated from the

reddening of [HII] regions or comparing the integrated Hα and thermal radio fluxes

(e.g., Ruffle et al., 2004). The nuclear regions of galaxies and the starburst regions

found in many mergers, can have much higher extinctions than those calculated for

normal galaxies. The emission line flux only traces the most massive stars requiring

the extrapolation of the Initial Mass Function (IMF) to lower stellar masses. The


[NII] doublet (6548 A and 6584 A) are very close to the Hα emission line and are

sometimes blended together. When separated high [NII]/Hα ratios can suggest

photo-ionisation due to the presence of an Active Galactic Nucleus (AGN) (Veilleux

et al., 1994).

While the Hα emission line is the strongest and hence most commonly used, any

hydrogen recombination line can be used, Brγ and Brα hydrogen emission lines in

Infrared wavelengths are often used for dusty regions. At higher redshifts the Hα

emission lines become unobservable in optical spectra (z & 0.4) and the higher order

Balmer lines such as Hβ or the [OII] doublet are substituted.

Using the Hβ emission line has essentially the same strengths and weaknesses

as the use of the Hα line. It too is sensitive only to the most massive stars and

suffers from the same dependence on dust extinction. In fact, Hβ encounters more

interstellar dust attenuation and is slightly more sensitive to the underlying stellar

absorption. Kennicutt (1992) regards its use as limited in normal galaxies, due to the

difficulty in accounting for the underlying stellar absorption, although population

synthesis models can try to account for this (Tremonti et al., 2004). There is a

strong correlation between the equivalent widths of Hβ and Hα+[NII] (Kennicutt,

1992). [OIII] has been used as a crude estimator of SFR but shows such a large

dispersion in relations to Hα that it has little significance (Kennicutt, 1992).

2.3.2 Ultraviolet continuum emission from hot stars

Young stars (< 107 yr) contribute most of the Ultraviolet (UV) flux in a galaxy,

hence the UV continuum in the range 1300-2500A is an indicator of the galaxies

SFR. This method allows the tracing of stars that are not hot or massive enough

to produce [HII] regions. The SFR in this way can be found using the relation of

Kennicutt (1998b),

SFR(UV) (M⊙yr−1) = 1.4 × 10−28Lν (erg s−1Hz−1), (2.2)

where Lν is the total luminosity per frequency interval.

While this method is undoubtedly a useful indicator it has several drawbacks.


The most serious of these is that the UV flux is very sensitive to interstellar extinc-

tion, meaning that the UV spectrum is of little use in the dusty starburst regions

of galaxies. The wavelength band used is also visible from the ground only for high

redshift systems.

2.3.3 Infrared thermal emission

Infrared (IR) emission in the 8–1000 µm band in star forming galaxies can arise

from three different processes, (a) emission from dust heated by young OB stars,

(b) emission from the photospheres of evolved stars as they lose mass, and (c) from

dust distributed throughout the interstellar medium, which is heated by the general

stellar radiation. The absorption cross section of the dust is highly peaked in the

UV and the absorbed radiation is re-emitted in the IR. If it is assumed that young

stars dominate the radiation field in the UV and visible bands, then the last two of

these processes are negligible. It is then also assumed that the opacity of the dust

in a galaxy is infinite, then the IR SFR is a good representation of the actual galaxy

SFR. The relation of Kennicutt (1998b),

SFR(IR) (M⊙yr−1) = 4.5 × 10−44LIR (erg s−1), (2.3)

where LIR is the total Ir luminosity in the 8-1000µ m band, can be used to gain the

IR SFR.

Calibration of the SFR for normal galaxies is not an easy task. The dust grains

absorb radiation with a broad range in wavelengths and hence radiation from young

and old stars. Conclusively separating the star forming component has proven elu-

sive. However, in the case of dusty starburst regions, the young stars dominate,

and the optical depth of the dust is so high that the IR emission is effectively the

bolometric luminosity of the starburst.

2.4. Star formation in interacting galaxies 27

2.3.4 X-ray Luminosity

It has been shown (e.g., Grimm, Gilfanov, & Sunyaev, 2003; Gilfanov, Grimm, &

Sunyaev, 2004) that high-mass X-ray binaries (HMXB) can be used as SFR indi-

cators. The X-ray luminosity (Lx) distribution of HMXBs can approximately be

described by a luminosity function which is a power law with a slope of ∼ 1.6 and

a cut off at log(Lx) ∼ 40.5, the normalisation of which is proportional to the SFR.

The 2-10 KeV Lx of a normal galaxy with sufficiently high SFR/M∗ ratio, where M∗

is the total stellar mass, is dominated by the emission from HMXBs. Therefore, Lx

can be used as a SFR indicator for normal galaxies. The Lx–SFR relation is only

linear for higher SFRs, the break in the relation occurring at SFR ∼ 4.5 M⊙ yr−1

or Lx ∼ 3 × 1040 erg s−1. In the linear regime the SFR of stars with M > 5 M⊙ is

given by,

SFR(Lx) (M⊙yr−1) =L2−10KeV

6.7 × 1039 (erg s−1), (2.4)

where L2−10KeV is the X-ray luminosity in the range 2-10 KeV. However, contamina-

tion of the SFR from the emission of the central supermassive black holes in which

even low luminosity AGNs can outshine the X-ray binaries and the contribution

of low-mass X-ray binaries which are unrelated to SFR and may be important for

low SFR can be a problem. The latter has been suggested by Gilfanov, Grimm, &

Sunyaev (2004) to be responsible for Ranalli, Comastri, & Setti (2003) obtaining a

linear Lx–SFR relation for all SFRs.

2.4 Star formation in interacting galaxies

2.4.1 Star formation mechanisms

The diversity of the star forming environments in interacting galaxies suggests that

several physical processes are responsible for the increased SFR seen in starburst

galaxies. Potential mechanisms for causing varying levels of increased SFR in dif-

ferent environments are discussed below.


Gravitational star formation thresholds

Nonlinear star formation features are seen in a wide range of interacting and normal

galaxies. An abrupt transition is seen in most late-type spirals where at a certain

radius SFR drops to very low values. Thresholds are also seen in gas-rich S0 galaxies

and low surface brightness galaxies. Kennicutt (1989) proposed that these thresholds

could be associated with large scale gravitational thresholds for the growth of density

perturbations. The Toomre parameter (Q) is the ratio of the critical density for star

formation at a given radius to the actual gas density. Regions that have Q ≫ 1

have suppressed star formation while regions with Q ≪ 1 would have unimpeded

star formation. However, regions with Q ∼ 1 would be stable but easily perturbed.

When galaxies interact, local compressions in density waves could cause the gas in

these stable regions to exceed the critical threshold, leading to an increase in SFR.

Cloud collisions

The variation in star formation thresholds can only account for a variation in SFR by

∼ 5%, which is not high enough to explain the large increases in strongly interacting

systems. When two galaxies closely interact, clouds of gas from the two galaxies

may collide with each other. Collision velocities may be high enough to cause

shocks, which can compress clouds inducing small-scale gravitational collapse and

star formation (e.g., Olson & Kwan, 1990). If the galaxies do not touch, but still

interact, small perturbations could cause gas clouds with orbits close to one another

to collide and start star formation (e.g., Lin, Pringle, & Rees, 1988). The rate of

collisions depends on the ratio between the lifetime of a cloud and the time interval

of the collision (Struck-Marcell & Scalo, 1987).

Tidally induced bars

One of the most critical pre-requisites for the most active starbursts is the transport

of large masses of interstellar gas at the centre of the merger. If one of two tidally

interacting systems has a large solid-body like rotation curve, then its partner can

induce a bar which out-lives the interaction itself. This can channel gas into the

nuclear region perhaps leading to a nuclear starburst (Noguchi, 1988). The gas and


star formation is often found in nuclear rings of dense young star clusters known as

“hotspots” or twin “peaks” (Kenney, 1994) often surrounding an AGN. This process

is unlikely to produce very luminous starbursts but may be important in the lower

level nuclear activities of many interacting galaxies.

2.4.2 Environmental influences

The environment of a galaxy is an essential ingredient of its evolution and SFR

properties. The relations between the density of galaxies, the presence of an intra

cluster medium (ICM), gas reserves, temperature and the velocity of encounters in-

fluence the resulting SFR, either enhancing or suppressing the rate. Many studies

of Hα and IR have shown increased SFR in merging and interacting galaxies (e.g.,

Bushouse, 1987; Kennicutt et al., 1987; Xu & Sulentic, 1991; Liu & Kennicutt, 1995).

On average the equivalent widths of the interacting galaxies show an enhancement

in SFR of approximately double that of an isolated sample. The majority of in-

teractions show only modest enhancements. However, they range from practically

no SFR enhancements to systems where a significant fraction of their total stellar

mass is star forming. Some of the main interacting processes which may influence

the onset of the above mechanisms are described below.

Galaxy Harassment

One of the most important influences on induced SFRs in galaxy-galaxy interac-

tions is tidal in nature, where the gravitational attraction of galaxies influence each

other. Multiple close encounters between galaxies at high speeds can deform gas

clouds and/or cause them to collide leading to an increased SFR. Moore et al. (1996)

used high resolution numerical simulations to study the effect of these multiple en-

counters and termed the phrase “galaxy harassment”. They conclude that “galaxy

harassment has the potential to change any internal property of a galaxy within a

cluster, including the gas distribution and content, the orbital distribution of stars

and the overall shape”. From these early results galaxy harassement has been inves-

tigated in numerous papers and used to explain the morphological transformation

of galaxies in clusters, in particular the formation of dwarf ellipticals, and even as


a source of fuel for quasars (e.g., Lake & Moore, 1999; Matkovic & Guzman, 2003;

Davies, Roberts, & Sabatini, 2005; Haines et al., 2006b). Observationally galaxy

harassment can be seen on galaxies with long tidal tails, drawn out by the close

encounters and rings around a stellar bar.

Tidal influence of a cluster potential

Galaxies falling into a cluster potential will experience a strong differential force the

strength of which depends on the galaxies orbit. The tidal force experienced is of

the order of,

Ftide ∼GM(r)

r3∼ σ2

cl

r2, (2.5)

where σcl is the cluster velocity dispersion, r is the distance from the cluster centre,

M(r) is the enclosed mass within radius r and G is the gravitational constant. The

tidal forces of the cluster potential can cause density waves in the gas of the infalling

galaxies leading to enhanced star formation where the densities become high enough.

Strangulation

It has been shown that galaxies can be surrounded by a halo of hot gas with a

temperature of up to a few million degrees Kelvin (e.g., Pedersen et al., 2006).

However, warm halos of gas with a temperature of a few hundred thousand degrees

Kelvin, which is too cool to be seen in X-ray detections and too warm to be seen

in radio detections, may be present around most galaxies. This halo of warm gas

would provide a reserve of gas which can be used to fuel star formation in the future.

As a galaxy falls into a cluster potential well, tidal effects can strip this reserve of

gas from the halo. This will result in a “strangulation” (e.g. Larson, Tinsley, &

Caldwell, 1980) of star formation, where star formation in the disk continues until

gas in the disk of the galaxy is used up, with no reserve of gas to fuel further star

formation. More massive galaxies will be more able to retain their warm gas haloes.


Ram pressure stripping

As a galaxy falls in towards the centre of a cluster it will encounter the ICM. The

ICM is hot gas which has been ejected from galaxies by early supernovae-driven

winds. In the centres of clusters the density of the ICM is high enough that the

galaxies moving through it will experience a strong drag force known as ram pressure.

Ram pressure can strip the gas from the disk of a galaxy causing the suppression

of star formation at the current time. Gunn & Gott (1972) give the conditions for

ram pressure stripping to be if the force due to ram pressure exceeds the restoring

gravitational force, given by,

Pram ≥ 2πGσstarσgas, (2.6)

and,

Pram = ρicmV 2gal, (2.7)

where Pram is the ram pressure, G is the gravitational constant, σstar is the stellar

surface density, σgas is the surface density of the gas, Vgal is the velocity of the galaxy

and ρicm is the density of the ICM.

Mergers

Evidence for the merging of galaxies in clusters has been demonstrated optically and

with X-ray data (e.g. Mahdavi et al., 1996; Mohr, Geller, & Wegner, 1996). This

is consistent with the hierarchical growth of structure with highly evolved galaxies

being found in clusters which are not yet in equilibrium. The process of merging can

cause bursts of star formation through effects such as cloud collisions. Larger galax-

ies have a greater merger cross section and hence mergers between dwarf galaxies

will be rare. Gnedin (2003) show that the number of close encounters experienced

by a galaxy can be given as,

Nenc ≈Ng

4π3

R3cl

πR2g

√2σcltH , (2.8)


where σcl is the cluster velocity dispersion, Rcl is the cluster virial radius, Ng is the

number of galaxies in the cluster and tH is the Hubble time. The probability of a

merger is then given by,

Pmer ∼ Nenc

(

σg

σcl

)4

, (2.9)

where σg is the galactic velocity dispersion.

Evaporation

As the cool gas in a galaxy encounters the hot ICM the galaxy can lose the gas

through evaporation. Fujita & Goto (2004b) show the time scale of the evaporation

of the cool gas can be given as,

te ≈3kbTicmMcold

2µmH |L|, (2.10)

where kb is the Boltzman constant, Ticm is the temperature of the ICM, µ(= 0.6) is

the mean molecular weight, mH is the Hydrogen mass, Mcold is the mass of cold gas

in the galaxy and L is the energy flux from the hot ICM surrounding the galaxy via

thermal conduction. The loss of the cool gas will curtail the ability of the galaxy to

form stars.

Active galactic nuclei

The process of interaction between galaxies can also trigger non-thermal nuclear

activities, creating active galactic nuclei (AGN). These AGN and the nuclear star-

bursts are closely intertwined and occur together in many interacting and normal

galaxies. However, it has been shown that galaxies dominated by nuclear star for-

mation are more prevalent in interacting systems (Sekiguchi & Wolstencroft, 1993),

and galaxies with AGN or composites may be as low as 15% (Brinchmann et al.,

2004) overall.

2.5. A star formation index from 2dFGRS spectra: the η parameter 33

2.5 A star formation index from 2dFGRS spectra:

the η parameter

The flux calibration of the 2dF spectra is unreliable due to instrumental limita-

tions. The calibration of fibre spectra is difficult to achieve due to, (a) astromet-

ric/positioning errors, which combined with the small fibre aperture prevent re-

producible sampling of each galaxy’s light distribution, (b) chromatic variations in

distortion, and (c) residual errors in the atmospheric dispersion correction (see Col-

less et al., 2001). Consequently a comprehensive study of the shape of the spectral

continuum is not possible. In order to find a parameter sensitive to SFR that can be

extracted from the uncalibrated 2dFGRS spectra, a Principal Component Analysis

of the galaxy spectra is the best method of gaining spectroscopic data . This essen-

tially measures the strength of the emission and absorption lines while remaining

insensitive to the continuum.

2.5.1 The Principal Component Analysis

Madgwick et al. (2002) initially took all the 2dFGRS observations until January

2001. This comprised a total of 111,404 galaxy spectra in the northern region and

60,062 in the southern region. They removed those galaxies which did not have an

accurate redshift (Q < 3, which is those galaxies which have a redshift which is,

probable, reliable, or reliable with a high quality redshift (see Colless et al., 2001))

, repeated observations and spectra with a signal to noise ratio of less than or equal

to 10. With a redshift cut of z≤ 0.15 to avoid corruption due to sky emission and

atmospheric absorption this left a total sample of 75,589 galaxies.

From this sample they defined a new parameter η based upon a Principal Com-

ponent Analysis (PCA) of the galaxy spectra. PCA is a statistical technique which

is used to reduce the dimensionality of the data to summarise the parts that are

useful to the user. In this case it does this by identifying the components of the

spectra that best discriminate between the galaxies. A detailed description of the

technique can be found in Glazebrook, Offer, & Deeley (1998).

The significance of each successive principal component was found to drop off


so sharply that the first two components retained two-thirds of the total variance

within the population. Thus from the initial 738 channels needed to describe each

spectrum, now only 2 were needed. The principal components were determined from

a subsample of the main sample, and these used to find the projections of the rest

of the sample. The subsample was chosen to have an absolute magnitude limit of

–18.0 corresponding to a redshift of approximately 0.1. This makes the process less

prone to bias from relationships between the luminosity and type of galaxy.

It was found that the first eigenspectrum derived from the PCA contains approx-

imately an equal contribution from both the continuum and the emission/absorption

lines. However, the second eigenspectrum is dominated by the emission and absorp-

tion lines. Therefore by taking linear combinations of the two, the line features can

be maximised, see Fig. 2.1. By maximising the emission and absorption features

they were in effect high-pass filtering the spectra. This meant that the projec-

tion was relatively stable to uncertainties in continuum measurements. Therefore,

once the projection was chosen, the η parameter was defined as: η = apc1 − pc2.

Where pc1 and pc2 are the first and second projections onto the principal axes and

a is a constant which maximises the absorption and emission features. Identifying

the most stable projection in the pc1, pc2 plane between repeated pairs of spectral

observations gave a value of a = 0.5 ± 0.1.

By comparing the values from approximately 2000 repeat observations an es-

timate of the uncertainties in the PCA was obtained. The difference in the two

projections between repeat observations had 1σ dispersions of 2.9 and 1.7 for pc1

and pc2 respectively. However the combination of the two in the η parameter is

greatly reduced having a 1σ dispersion of 0.7.

The analysis has been expanded to now contain 192,982 galaxies with an η value

from a total of 245,591 galaxies in the final catalogue.

2.5.2 Relationships with other parameters

Madgwick et al. (2002) plotted the relation between the η parameter and its mor-

phological type for the spectrophotometric standard galaxies in Kennicutt’s atlas

(Kennicutt, 1992). It can be seen in Fig. 2.2 that there is a relation between the


Figure 2.1: The first two principal components identified from the 2dF galaxy spectra and the

linear combinations which isolate either (a) the continuum slope or (b) the line features (Madgwick

et al., 2002). (§2.5.1)

morphological type and the value of η. Thus our own galaxy, the Milky way (Sb),

would have a η of between approximately 0 and 2. It is also possible to see that

a histogram of the η parameter is bimodal. The first peak corresponds to mainly

E/S0 galaxies, which would be consistent with little or no star formation at the

current time at these low η values. Approximately 40% of the galaxies are in the

first passive galaxy peak.

Madgwick et al. (2003) compared the value of η derived for each galaxy to the

equivalent width of the Hα emission-line spectra. It can be seen in Fig. 2.3 that

with some scatter there is a strong linear correlation between the two quantities.

A Hα EW of 0.0 corresponds to η ≈ −2.0 and A Hα EW of 50.0 corresponds to

η ≈ 7.0.

Madgwick et al. (2003) also compare the η with the birth rate parameter, b,

which is the ratio of the current SFR to the past averaged SFRs. They initially

derive b using a simple model of the star formation history in terms of an exponen-

tial function of time (Bruzual, 1983) with a Kennicutt (1983) initial mass function of:


Figure 2.2: (Top) The distribution of η projections for the volume-limited sample of 2dF galax-

ies.Vertical lines show the devisions in η that correspond roughly to E/S0, early type S, late type

S and Irr, used in the analysis of Madgwick et al. (2002) (Bottom) The η projections calculated for

a subset of the Kennicutt Atlas galaxies. This plot is taken from Madgwick et al. (2003). (§2.5.2)

Figure 2.3: The correlation between η and the equivalent width of the Hα emission line for a

sample of high signal-to-noise ratio emission-line spectra (Madgwick et al., 2003). (§2.5.2)


SFR(t) =1

τe−(t−tf )/τ , (2.11)

where tf is the time at which star formation first commences and τ is the charac-

teristic timescale of the star formation.

The PEGASE software package is used to realize the model and deals with other

tasks such as determining the strengths of nebula emission lines and dust extinction.

Spectral histories of a given galaxy are compiled for a range of formation times (0–20

Gyr) and lengths of star formation activity (0–2 Gyr). The value of b is determined

from:

SFR(t)

〈SFR(t)〉past=

(t − tf)

τ

e−(t−tf )/τ

(1 − e−(t−tf )/τ )= b. (2.12)

The same analysis is also performed using a semi-analytic model. In the hier-

archical model for the universe galaxies have built up from mergers and accretion.

Mergers can trigger bursts of star formation, which in turn may inhibit future forma-

tion by expelling gas from the galaxy on stellar winds. This model can be convolved

with stellar population models to produce model spectra. Madgwick et al. (2003)

use a multi-metalicity GISSEL model (Bruzual, 1983) and a Salpeter IMF. They

construct a mock 2dF catalogue of 2,611 model galaxies with the same magnitude

limit, wavelength coverage, spectral resolution and redshift range as the actual 2dF-

GRS. They derive the principal components of the mock catalogue and the birth

rate parameter b for each galaxy. They show that b has a strong relationship to the

η parameter in both the simple model and the semi-analytic model. This relation is

shown for the semi-analytic model in Fig. 2.4. It can be seen that galaxies with an

η of less than approximately –1.4 have a value of b < 0.1, where the current SFR is

only 10% of what it was in the past.


Figure 2.4: (Left) η plotted versus b for each galaxy in the SAM mock-galaxy catalogue. (Right)

The mean value of η versus b for these galaxies (the dashed lines show the 1 σ uncertainties). Also

shown on this plot (dotted lines) are the cuts in η used in Madgwick et al. (2002) to calculate

the 2dFGRS luminosity functions per spectral type. It can be seen, for example, that the Type I

galaxies of that paper (η < −1.4) correspond to galaxies with b < 0.1, or, alternatively, galaxies

with current star formation activity that is only 10 per cent of their past-averaged rate. Figure

taken from Madgwick et al. (2003). (§2.5.2)

2.5.3 Separating the star-forming and non star-forming pop-

ulations

As mentioned previously (also see Fig. 2.5) a histogram of the η parameter is ex-

tremely bimodal. The first narrow peak corresponding to the non star-forming

galaxies (approximately 30 % of all z < 0.1 galaxies) and the wider second peak the

galaxies with current star formation.

To obtain the probability that a given galaxy falls within the first or second

peak, P (η), a series of likely functions were fitted to the two peaks such that,

P(η) = αg(η) + (1 − α) f(η), (2.13)

where f(η) is a function of η to fit the first peak, g(η) is a function of η to fit the

second peak and α is a constant. P (η) can be maximised such that,


Figure 2.5: A histogram of the η parameter for all 2dFGRS galaxies with z < 0.1 binned in 0.1

η bins. (§2.5.3)

L =∑

lnP (η). (2.14)

The first peak was fitted with a standard Gaussian function such that,

f(η) =1

σ√

2πe

−(η−µ)2

2σ2 , (2.15)

where µ is the position of highest point of the peak and σ is the standard deviation

of the peak.

The second peak was fitted with an extreme value distribution such that,

g(η) =e(σ−η)/µ−e(σ−η)/µ

µ. (2.16)

L was fitted using the NAG routine E04JYF and the resulting fit can be seen as

the dashed line in Fig. 2.6. However, it can be seen in Fig. 2.7 when the values of µ

and σ obtained are used to plot the individual functions the Gaussian seen as the

dashed red line is not an appropriate fit to the first peak.


Figure 2.6: Composite fit to the 2dFGRS η parameter distribution. The resulting fit shown

as the dashed orange line is a combination (eq.Fig. 2.13) of a Gaussian and an extreme value

distribution. The histogram shown is for the entire 2dFGRS binned in 0.1η bins. (§2.5.3)

Figure 2.7: Individual fits to the 2dFGRS η parameter distribution. The red dashed line is the

Gaussian function and the dashed blue line the extreme value distribution plotted with the values

of µ and σ obtained from the composite fit. The histogram shown is for the entire 2dFGRS binned

in 0.1η bins. (§2.5.3)


The above fitting of a sum of two distributions did not lead to a more elegant

separation of the star-forming and non star-forming populations. A KMM algorithm

(Ashman, Bird, & Zepf, 1994) could also have been used to partition the data in two

subpopulations. However in the end it was decided that a complex solution to the

bimodality was not needed and a transitional value set at η = −1.4, below which all

galaxies will be classified as “passive” was chosen. This corresponds to, the divide

between E/S0 and Sa galaxies in Fig. 2.2, a Hα EW∼ 3 in Fig. 2.3 and a b < 0.1 in

Fig. 2.4, where the current SFR is only 10% that it was in the past.

Chapter 3

Viscount Horatio Nelson: “Thank God I have done my duty.”

Supercluster structure

Superclusters are an essential tool to study the largest-scale density perturbations

that have given rise to structure in the Universe (e.g., Bahcall, 2000). These are

particularly interesting since they have always evolved in the linear regime and can

be analytically tractable. Superclusters can be useful in quantifying the the high-end

mass function of collapsing systems and ratio of mass to light on the largest scales,

thus being useful in discriminating between dark matter and structure formation

models (e.g., Kolokotronis, Basilakos, & Plionis, 2002; Bahcall, 1988).

3.1 Minimal spanning tree supercluster structure

Superclusters are expected to be predominantly filamentary structures. Numer-

ical simulations of the evolution of large-scale structure (e.g., Bond, Kofman, &

Pogosyan, 1996; Colberg, Krughoff, & Connolly, 2005), as well as the analysis of

large-volume surveys like the 2dFGRS (e.g., Pimbblet, Drinkwater, & Hawkrigg,

2004) or studies of individual systems of superclusters (e.g., Bagchi et al., 2002;

Ebeling, Barrett, & Donovan, 2004) show the pre-eminence of filamentary struc-

tures. Nevertheless, supercluster catalogues are usually constructed (e.g., Einasto

et al., 1994; Zucca et al., 1993) using percolation or friends-of-friends algorithms

which do not take this geometrical feature into consideration.

Recently, Raychaudhury et al. (2007) have compiled a catalogue of supercluster-

size structures from a redshift survey of Abell clusters (z < 0.1) using the minimal

42

3.1. Minimal spanning tree supercluster structure 43

spanning tree statistic, which contains all the information used in a percolation anal-

ysis (Bhavsar & Splinter, 1996), and is particularly sensitive to filaments (Bhavsar

& Raychaudhury, 2000).

In this Chapter we investigate the structure of the three richest superclusters in

the catalogue of Raychaudhury et al. (2007), Horologium-Reticulum, Shapley and

Pisces-Cetus. We also gain estimates of the mass overdensity within each of the

superclusters.

3.1.1 The Pisces-Cetus supercluster

More than a decade ago, in a series of papers, Tully (1986, 1987, 1988) pointed

out the Pisces-Cetus supercluster to be one of the five richest systems of clusters

of galaxies in the z < 0.1 Universe, and speculated that it could be as large as

300 h−170 Mpc across, and might include the Local Group. Subsequent work (e.g.,

Zucca et al., 1993; Einasto et al., 1994) has pointed out interesting features of

significantly smaller substructures of this remarkable web of galaxies, groups and

clusters, and at least one unusually large void (Burns et al., 1988).

The Pisces-Cetus supercluster is found to straddle the 2dF galaxy redshift survey

(Colless et al., 2003) [2dFGRS] and the Sloan Digital Sky Survey (Abazajian et al.,

2005) [SDSS] regions.

In the supercluster catalogue of Raychaudhury et al. (2007), the Pisces-Cetus

supercluster occupies a region of about 700 sq. deg. of the (equatorial) southern

sky. While using the Minimal Spanning Tree (MST) in constructing this catalogue,

if a maximum edge-length of 20 h−1100 Mpc is used, the system breaks up into two

filaments (A, B) of 11 and 5 clusters respectively, at mean redshifts of 0.0625 and

0.0545 respectively. If, however, adjacent clusters on the tree are allowed to be

separated by a distance of up to 25 h−1100 Mpc, the supercluster becomes a long

filament of 19 clusters at a mean redshift of 0.0591, making the supercluster the

third richest in the catalogue (following the Shapley and Horologium-Reticulum

superclusters). This is illustrated in Fig. 3.1, where the clusters excluded by the

former consideration are shown to be connected to the main tree by dashed lines.

The clusters comprising the Pisces-Cetus supercluster from the MST analysis of


Raychaudhury et al. (2007) form the core of our sample, and are listed in Table 3.1.

Unlike MST analyses of galaxy catalogues, where completeness is an important con-

sideration, the supercluster list obtained in this catalogue is considered reasonably

complete since it arises from an analysis of rich Abell clusters in the volume closer

than z < 0.1 (Galactic latitude |b| > 20).

To the member list of the Pisces-Cetus Supercluster from the above list, we

added a few clusters, in the same volume as the filament, from the Supplementary

Abell cluster catalogue (Abell et al., 1989) and the Edinburgh-Durham Southern

Galaxy Cluster Catalogue (Lumsden et al., 1997). These extra clusters were taken

as potential members of the supercluster if their redshift as derived in §3 was found

to be consistent with the other members.

A plot of these clusters within the supercluster region and redshift range, in-

cluding the connecting MST, can be seen in Fig. 3.1. Also plotted are the groups

of galaxies in the region of the supercluster covered by the 2dFGRS (δ < −25 )

from the 2dFGRS Percolation-inferred Galaxy Group (2PIGG) catalogue (Eke et al.,

2004), which are seen to follow a filamentary structure (though not necessarily the

tree defined by the MST), as expected from numerical simulations where groups

are seen to preferentially form on filaments and move along filaments to fall into

clusters. For comparison, Fig. 3.2 shows all galaxies with spectroscopic redshifts

from the SDSS and 2dFGRS catalogues, where only galaxies within 3000 km s −1 of

the upper and lower redshift bounds of the supercluster have been plotted. Over-

densities of galaxies are clearly visible in the regions around the richer clusters and

the filamentary structure of the supercluster is also visible.

A combined look at Figs. 3.1 and 3.5 through 3.7 reveals that the supercluster

is made of two main filaments. From Fig. 3.5 which plots redshift against Right

Ascension for the groups and clusters in the region, it is evident that the filament

containing A85 is at a lower redshift than the longer filament, which has A133 at the

near end and A2716 at the more distant end. The poorer clusters E0332 and S1155,

appear to be in a clump separated from both of the main filaments, with a filament

of groups joining these three clusters to the principal filament. These trends are also

seen in Fig. 3.7 which plots redshift against declination for the groups and clusters


Figure 3.1: Clusters of galaxies belonging to Pisces-Cetus supercluster. The minimal spanning

tree used to identify the supercluster (Raychaudhury et al., 2007) is shown connecting the clusters.

Edges in the tree with length 20 h−1

100<L≤25 h−1

100Mpc are shown as dashed lines. The groups of

galaxies (2PIGG) identified from a friends-of-friends analysis of the 2dFGRS (Eke et al., 2004) are

shown as little circles between redshifts of 13507 and 22810 km s−1, which is ± 3000 km s−1 from

the lowest/highest cluster redshifts of chain A 20 h−1

100Mpc links. (§3.1.1)

in the region. Although, the filament of groups linking the E0332, S1155 clump to

the main chain is less visible.

It is also possible to see the filamentary structure and concentration of galaxies at

the cluster positions in Fig. 3.3. All of all the galaxies in the SuperCOSMOS galaxy

catalogue within the Pisces-Cetus supercluster bounds are shown. All galaxies had

to be classified as a galaxy in each of the three bands B, I and R2. In addition, the

quality of the detection had to be less than 128 in each band and gCorMagB < 20.0,

where gCorMagB is the magnitude if the object is assumed to be a galaxy. By

eye, circular concentrations can be seen at the junction of long thin filaments at the

positions of Abell clusters. This is confirmed in Fig. 3.4 showing the density contours

of the galaxies in Fig. 3.3. Green contours showing the higher density regions can

be seen at the positions of Abell clusters.

Fig. 3.6 shows all the galaxies with redshifts from 2dFGRS and ZCAT in the

declination range −32 < δ < −20. The diagram shows clearly the filamentary

nature of the supercluster and the positions of the Abell clusters on the filaments.


Figure 3.2: All galaxies with measured redshifts from the 2dFGRS and SDSS surveys in the

Pisces-Cetus region, between redshifts of 13507 and 22810 km s−1, which is ± 3000 km s−1 from

the lowest/highest cluster redshifts of chain A 20 h−1

100Mpc links. The SDSS reaches down to

δ = −10 in this R.A. range, and covers the clusters A85, A87 and A117. The SDSS reaches up

to δ = −25, and thus a large part of the supercluster falls in the gap between the two surveys,

except for the occasional isolated two-degree fields of the 2dFGRS. (§3.1.1)

There are some clusters not obviously associated with overdensities, these are in the

declination range not covered by the 2dFGRS.

3.1.2 The Horologium-Reticulum Supercluster

Harlow Shapley (Shapley, 1935) was the first to note that the Horologium region was

abnormally rich in galaxies. Since then further studies have confirmed the presence

of an overdense region of clusters and galaxies (e.g., Lucey et al., 1983; Einasto et

al., 2003; Fleenor et al., 2005, 2006). Lucey et al. (1983) were the first to obtain

redshifts and find velocity dispersions for the clusters in the Horologium-Reticulum

supercluster region, thus confirming the superclusters existence. More recently the

region has been shown to have entered the non-linear regime with a mass overdensity

of 2.4 (Fleenor et al., 2005).

In the supercluster catalogue of Raychaudhury et al. (2007) if a maximum edge

length of 25 h−1100 Mpc is used in the MST analysis the Horologium-Reticulum su-


Figure 3.3: All galaxies in the SuperCOSMOS galaxy catalogue within the Pisces-Cetus super-

cluster bounds. All galaxies are classified as a galaxy in each of the three bands B,I and R2. In

addition the quality of the detection is less than 128 in each band and gCorMagB< 20.0 (magnitude

if the object is assumed to be a galaxy). (§3.1.1)


Figure 3.4: Density contours of all galaxies in the SuperCOSMOS galaxy catalogue within

the Pisces-Cetus supercluster bounds. All galaxies are classified as a galaxy in each of the three

bands B,I and R2. In addition the quality of the detection is less than 128 in each band and

gCorMagB< 20.0 (magnitude if the object is assumed to be a galaxy) Contours range from 75 to

225 galaxies per 1 degree2 bin in 10 increments of 15 galaxies. Contours are shown in red below

and green for and above the 120 galaxies per bin level. (§3.1.1)

Figure 3.5: Clusters of galaxies belonging to Pisces-Cetus supercluster, covering the declination

range −32<δ < −9). The 2PIGG groups of galaxies are shown as little circles, but only in the

declination range covered by the 2dFGRS −32<δ < −25). (§3.1.1)


Figure 3.6: Galaxies with redshifts (mostly from 2dFGRS, see §3) in the Pisces-Cetus supercluster

region (Declination range −32<δ < −20). The mean positions of the clusters in the supercluster

are marked. The 2dFGRS only goes up to δ < −25, which is why some of the clusters don’t seem

to be associated with obvious concentrations. (§3.1.1)

Figure 3.7: Clusters of galaxies belonging to Pisces-Cetus supercluster, covering the Right As-

cension range 345 <δ < 20). The 2PIGG groups of galaxies are shown as little circles. (§3.1.1)


Figure 3.8: Clusters of galaxies belonging to Horologium-Reticulum supercluster. The minimal

spanning tree used to identify the supercluster (Raychaudhury et al., 2007) is shown connecting

the clusters. Edges in the tree with length 20 h−1

100< L≤ 25 h−1

100Mpc are shown as dashed lines.

(§3.1.2)

percluster comprises 33 Abell clusters making it the richest in the catalogue. The

supercluster occupies approximately 1300 degrees2 of the equatorial southern sky.

The mean redshift of the supercluster is 0.067 but with a range in z from 0.0567

to 0.084 a lot of the structure is radial direction. The clusters comprising the

Horologium-Reticulum supercluster are those of the MST analysis of Raychaudhury

et al. (2007), and are listed in Table 3.2.

A plot of these clusters within the supercluster region and redshift range, in-

cluding the connecting MST, can be seen in Fig. 3.8. The radial nature of the

supercluster is evident with many clusters and links falling on top of each other in

R.A.-Dec. space.

For comparison, Fig. 3.9 shows all galaxies with spectroscopic redshifts from

the latest version of ZCAT, where only galaxies between 13000 km s −1 and 30000

km s −1 have been plotted. Overdensities of galaxies are clearly visible in the regions

around the richer clusters.

Fig. 3.11 and Fig. 3.10 clearly show the large radial component to the superclus-

ters structure using the redshift information described below.


Figure 3.9: All galaxies with measured redshifts from the latest version of ZCAT (http://cfa-

www.harvard.edu/∼huchra/zcat/) in the Horlogium-Reticulum region, between redshifts of 13965

and 28337 km s−1, which is ± 3000 km s−1 from the lowest/highest cluster redshifts. (§3.1.2)

Figure 3.10: Clusters of galaxies belonging the Horologium-Reticulum supercluster in R.A.-

redshift space, covering the declination range −63<δ < −35. (§3.1.2)


Figure 3.11: Galaxies with redshifts from the latest version (2005) of ZCAT in the Horologium-

Reticulum supercluster region (Declination range −63 < δ < −35). The mean positions of the

clusters in the supercluster are marked. (§3.1.2)

3.1.3 The Shapley supercluster

The clusters comprising the Shapley supercluster are those of the catalogue of Ray-

chaudhury et al. (2007). A plot of the resulting members including the MST links

can be seen in Fig. 3.12 and a list of the clusters can be found in table 3.3. Fig. 3.12

shows all galaxies with measured redshifts from NED in the region, overdensities of

galaxies at the cluster positions are clearly visible.

With a maximum edge length of 25 h−1100 Mpc in the MST analysis, the Shap-

ley supercluster forms one large structure of 29 Abell clusters which can be seen

in Fig. 3.12 at a mean redshift of z = 0.0476. Fig. 3.14 clearly shows that the

supercluster is separated into two sections in the radial direction. The main group

containing the core of A3555, A3556 and A3558 centred around 15000 km s−1 and

the smaller group containing A3571 is at approximately 12000 km s−1. While being

within the central regions in R.A.-Dec. space, A3546 is quite isolated in the radial

direction from the two main groups.


Figure 3.12: Clusters of galaxies belonging to the Shapley supercluster. The minimal spanning

tree used to identify the supercluster (Raychaudhury et al., 2007) is shown connecting the clusters.

Edges in the tree with length 20 h−1

100<L≤25 h−1

100Mpc are shown as dashed lines. (§3.1.3)

Figure 3.13: All galaxies with measured redshifts from NED in the Shapley supercluster region,

between redshifts of 10462 and 19480 km s−1, which is ± 3000 km s−1 from the lowest/highest

cluster redshifts of the main chain at a mean redshift of approximately 15000 km s−1. (§3.1.3)

3.2. Mean redshift and velocity dispersion 54

Figure 3.14: Clusters of galaxies belonging the Shapley supercluster in R.A.-redshift space,

covering the declination range −41<δ < −12. (§3.1.3)

3.2 Mean redshift and velocity dispersion

Positions from the NASA/IPAC Extragalactic Database (NED) were taken as a

starting point for the cluster centres, and then they were located on UK Schmidt

Telescope (UKST) BJ plates. The NED positions, particularly those from Abell et

al. (1989), were largely inadequate. Therefore, centres were determined from avail-

able X-ray data whenever possible, and from a visual inspection of the appropriate

UKST plates otherwise.

Redshifts were taken from all available sources including NED, ZCAT (http://cfa-

www.harvard.edu/∼huchra/zcat/), the second data release of the 6dF Galaxy Sur-

vey Database (Jones et al., 2005) [6dFGS DR2], the 2dF galaxy redshift survey

(Colless et al., 2003) and the second release (DR2) of the Sloan Digital Sky Survey

(Abazajian et al., 2005). In the case of Horologium-Reticulum supercluster addi-

tional redshifts were gained from Fleenor et al. (2005) and Fleenor et al. (2006). For

the Shapley supercluster the NED redshifts came largely from Kaldare et al. (2003).

Galaxies were initially extracted from these catalogues within an Abell radius

(2.14 h−170 Mpc, 1.5 h−1

100 Mpc) of the new cluster centres and filtered for repeated

galaxies. In the case of the very dense Shapley supercluster, an initial circle of

radius of 2.14 h−170 Mpc was tried around each cluster. If this did not overlap any


other clusters this was adopted as the extraction radius for galaxies. If an overlap

was present the size was modified accordingly till each extraction area was unique.

In the case of Abell 85/87 it has been shown (Durret et al., 2003) while Abell 85

is a strong X-ray source Abell 87 is not detected. It is likely that Abell 87 is in fact

a system of filaments and groups of galaxies merging with A85. Therefore, while

the same extraction was performed for A87 as the other clusters it is likely that

many of the extracted galaxies are members of the large merging cluster of Abell

85. Because of this ambiguity A87 is not used in our virial mass estimates described

below.

For clusters that have redshifts available for ≥ 4 galaxies, within the extraction

radius, mean recessional velocities were calculated, using an iterative process clip-

ping 3σ about the median, and finally calculating the mean. If ≥ 12 galaxies with

known redshift remained, the velocity dispersion of the cluster and its error were

calculated, using a method that takes into account observational errors on individual

redshift measures (Danese, de Zotti, & di Tullio, 1980). The dispersion is given by,

σ2‖ =

∑

i

υ2‖i

(n − 1)− δ2

(1 +ν‖c)2

, (3.1)

where υ‖ is the radial velocity of a galaxy relative to the mean cluster velocity, ν‖ is

the mean cluster velocity, n is the number of galaxies in the cluster and δ is the sum

of the uncertainties on the individual galaxy radial velocities. The 68% uncertainties

on the velocity dispersion are given by,

(∆σ‖±)2 ∼=[( ν

χ2∓− 1

)1/2]2

σ2‖ +

δ2∗n

(

1 +δ2∗

2σ2‖

)

, (3.2)

where δ2∗ = δ2

(

1+ν‖c

)2 , n is the number of galaxies in the cluster, ν is n − 1 and χ2∓

is taken from the table of Danese, de Zotti, & di Tullio (1980) for small values or

from,

χ2±∼= ν

[

1 − 2

9ν± χp

( 2

9ν

)1/2]3(3.3)


for χ2 > 30.

The resulting mean velocities, velocity dispersions and the number of cluster

members used to calculate them can be found in Table 3.1, Table 3.2 and Table 3.3,

for each cluster belonging to the Pisces-Cetus, Horologium-Reticulum and Shapley

superclusters respectively.

Our mean velocities for the clusters of the Horologium-Reticulum supercluster

are in good agreement with those of Fleenor et al. (2006). 16 out of 18 clusters agree

to within 240 km s−1 and the remaining 2 to within 370 km s−1.

The velocity dispersions of Fleenor et al. (2006) are in reasonable agreement with

our own, 5 out of 7 of the clusters agreeing within 170 km s−1. While the remaining

two, A3109 and A3164 agreeing within 441 km s−1 and 286 km s−1 respectively both

have some ambiguity on the edges of the cluster in the velocity histograms of figs

3.18 and 3.19.

Velocity histograms for the clusters can be seen in figs. 3.16 to 3.19. Where

more than a peak is obviously present, the velocity dispersion of the peak closest to

the current literature value of the clusters mean velocity has been adopted. When

an accepted current mean velocity is unavailable, the peak closest to the mean

recessional velocity of the supercluster has been adopted.

Fig. 3.16 shows the radial velocity histograms for the Pisces-Cetus supercluster.

Fig. 3.19 shows the velocity histograms for clusters in the Shapley supercluster that

had an extraction radius equal to the Abell radius while Fig. 3.19 shows those with a

reduced extraction radius. The reduced extraction radius is shown in the top centre

of each clusters panel as a fraction of the Abell radius. Fig. 3.17 shows the velocity

histograms for the Horologium-Reticulum supercluster.

3.2.1 Models of Surface brightness

To obtain an estimate of the mass of each of the clusters (see §3.3), it was necessary

to obtain a surface brightness profile for each cluster. For all clusters belonging


Table 3.1: Clusters belonging to the Pisces-Cetus Supercluster

Cluster. R.A. Dec. cz # z Lx T Rich Survey σr r200 rv MNFW

(J2000) (J2000) km s−1 ×1044 ergs−1 keV km s−1 Mpc Mpc 1015 M⊙

A0014 00 15 10.9 -23 52 56 19665 13 0.51b 2.8b,∗ 0 - 643+185−100 2.01 3.85 0.72

A0027 00 24 52.1 -20 43 14 16287 6 <0.028d 1.0∗ 0 - 0.63 3.08

A0074 00 39 08.8 -22 19 49 19264 11 0.021a 1.1∗ 0 - 0.88 3.47

A0085 00 41 50.8 -09 18 18 16556 294 12.47c 6.2a 1 S 1016+44−39 2.08 0.82 0.67

A0086 00 42 40.0 -21 48 01 18911 12 0.094a 1.3∗ 0 - 1.71 3.67

A0087 00 43 01.0 -09 47 36 16535 194 1 S 987+54−46

A0114 00 53 27.5 -21 44 42 17696 24 0.055a 1.4∗ 0 - 525+100−65 1.57 2.95 0.34

A0117 00 55 51.9 -09 59 09 16424 101 0.26a 1.5∗ 0 S 604+47−38 1.77 3.13 0.45

A0126 00 59 53.8 -14 14 41 16274 11 0.027d 1.2∗ 1 - 1.31 3.06

A0133 01 02 41.2 -21 52 45 16507 20 3.81c 3.8a 0 - 687+146−90 1.97 2.97 0.69

A0151 01 08 51.1 -15 24 23 15982 73 0.70b 3.1b,∗ 1 - 699+66−52 1.58 1.01 0.32

A2660 23 45 16.0 -25 50 09 18724 17 0.049d 1.7∗ 0 0.73 800+189−111 2.29 3.41 1.00

A2683 23 57 36.7 -25 36 44 19625 11 0 0.88 0.65 3.96

A2716 00 03 01.3 -27 08 11 19810 77 0 0.85 812+75−59 2.27 3.84 0.77

A2734 00 11 19.5 -28 51 41 18486 141 2.22c 4.4b,∗ 1 0.82 848+55−46 1.64 0.62 0.38

A2794 00 37 38.1 -30 48 59 18298 34 1 0.97 365+56−40 0.73 0.39 0.04

A2800 00 38 09.4 -25 04 51 19054 79 1 0.81 567+52−41 1.67 3.43 0.36

A2824 00 48 34.0 -21 20 36 17460e 7 0.47b 2.8b,∗ 0 -

A4053 23 54 46.0 -27 40 18 19670 26 1 0.88 398+72−48 1.54 3.44

S1136 23 36 16.9 -31 36 20 18562 54 1.25b 3.7b,∗ 0 0.89 602+68−51 1.86 4.41 0.59

S1155 23 49 44.0 -29 07 13 14950 33 0 1.00 345+57−42 1.20 2.92 0.17

ED332 23 41 35.5 -29 14 11 15280 84 1.00 477+43−35 1.46 2.61 0.30

(1) Name of cluster (A*** and S*** Abell et al. (1989), ED332 Lumsden et al. (1997).

(2,3) Equatorial J2000 centres (we use centroids of X-ray emission where available).

(4) Redshift (see §3.2).(5) Number of cluster member redshifts used to find the mean cluster redshift ((e) Struble & Rood (1999) and

§3.2).(6)Bolometric X-ray luminosities ((a)Jones & Forman (1999). (b) Cruddace et al. (2002); (c) Reiprich & Bohringer

(2002); (d) Ledlow et al. (2003)).

(7) Temperature (∗=estimated from LX − T relation Osmond & Ponman (2004)).

(8) Abell richness (Abell et al. (1989)).

(9) Survey coverage [S=Sloan, Number= completeness in 2dFGRS field].

(10) Velocity dispersion (see §3.2).(11) r200 in h−1

70 Mpc (see Eq. (3.26)).

(12) Virial radius (see Eq. (7)).

(13) Cluster virial mass within an Abell radius (2.14 h−170 Mpc) (see Eq. (3.19)).


Table 3.2: Clusters belonging to the Horologium-Reticulum Supercluster

Cluster R.A. Dec. cz # z Rich σr r200 rv MNFW

(J2000) (J2000) km s−1 km s−1 Mpc Mpc 1015 M⊙

A2988 02 12 52.3 -47 08 24 19663 8 1 0.31

A3004 02 18 51.8 -47 59 57 19565 7 0 3.31

A3009 02 22 06.9 -48 33 50 19713 16 1 493+122−71 1.50 3.44 0.32

A3074 02 58 11.2 -52 43 42 21580 7 0 3.64

A3078 03 00 25.0 -51 50 53 21768 42 0 499+66−48 1.30 1.90 0.23

A3089 03 08 16.8 -36 42 31 19779 31 0 628+100−68 1.18 0.44 0.15

A3093 03 10 52.6 -47 24 19dx 24667 30 2 685+111−75 1.82 4.23 0.43

A3098 03 13 43.1 -38 18 03 25337 12 0 311+96−51 1.04 3.68 0.11

A3100 03 13 52.7 -47 47 34 18901 22 0 312+63−41 1.06 3.40 0.12

A3104 03 14 22.8 -45 25 23ex 21822 66 0 731+73−56 1.98 3.75 0.62

A3106 03 14 29.8 -58 05 48 19529 12 0 429+124−67 0.88 0.47 0.07

A3107 03 14 56.4 -42 41 07 19108 23 1 1045201127 4.10

A3108 03 15 44.9 -47 43 39b 18931 21 1 382+79−50 3.15

A3109 03 16 39.2 -43 51 19 18925 21 0 1520+209−148 1.31 4.80 0.20

A3110 03 16 31.1 -50 54 44 22489 7 0 3.63

A3111 03 17 51.6 -45 43 43 23257 47 1 931+114−84 2.35 3.89 0.87

A3112 03 17 57.8 -44 14 18dx 22401 82 2 1087+96−76 2.67 3.75 1.33

A3116 03 19 00.0 -42 56 02 24015 13 0 1334+407−212 3.48 4.60 2.66

A3120 03 21 56.4 -51 19 36 21247 5 0

A3122 03 22 18.6 -41 21 34fx 18427 102 2 872+68−55 1.70 0.38 0.37

A3123 03 23 00.0 -52 01 00c 18105 18 0 524+120−73 1.58 3.53 0.36

A3125 03 27 24.0 -53 30 00c 17998 75 0 789+74−58 2.10 3.29 0.80

A3128 03 29 51.5 -52 35 07gx 18010 198 3 840+45−39 1.53 0.62 0.33

A3133 03 32 42.0 -45 56 00c 21256 12 0 428+131−68 1.47 3.06 0.21

A3135 03 34 01.7 -39 00 54dx 18777 54 2 872+99−74 2.27 3.39 1.00

A3140 03 36 18.7 -40 37 20fx 18777 5 0 0.36

A3145 03 37 51.0 -38 01 12a 19144 7 0 0.26

A3158 03 42 53.5 -53 37 50dx 17758 138 2 994+66−55 2.41 2.93 1.16

A3164 03 45 52.6 -56 55 37ex 17769 18 0 861+196−117 2.14 2.76 0.84

A3202 04 00 14.9 -53 39 37a 20779 27 1 427+74−49 1.34 3.52 0.23

A3225 04 09 25.6 -59 36 55 16965 36 0 658+95−66 1.78 2.89 0.51

A3266 04 31 19.4 -61 26 50dx 17800 272 2 1209+55−48 2.08 0.81 0.75

A3312 05 03 54.1 -56 55 55a 2 2.52

(1) Name of cluster (A*** and S*** Abell et al. (1989)).

(2,3) Equatorial J2000 centres; (a)Abell et al. (1989), (b)Katgert et al. (1998), (c)(Fleenor et al., 2005),

X-ray centres; (dx)David, Forman, & Jones (1999), (ex)Ebeling et al. (1996), (fx)Bohringer et al. (2004),

(gx)Rose et al. (2002);

(4) Redshift (see §3.2).(5) Number of cluster member redshifts used to find the mean cluster redshift.



70 Mpc (see Eq. (3.26)).


(10) Cluster virial mass within an Abell radius (2.14 h−170 Mpc) (see Eq. (3.19)).


Table 3.3: Clusters belonging to the Shapley Supercluster

Cluster R.A. Dec. cz # z Rich σr r200 rv MNFW

(J2000) (J2000) km s−1 km s−1 Mpc Mpc 1015 M⊙

A1631 12 52 52.7 -15 24 46 13836 271 1 696+32−28 1.98 3.64 0.67

A1644 12 57 9.8 -17 24 1c 14268 129 1 982+67−56 1.89 1.00 0.57

A1709 13 18 50.6 -21 25 34 15725 12 0 404+127−71 0.75 0.32 0.05

A1736 13 26 58.9 -27 10 13b 13462 111 0 1157+86−70 2.85 3.40 1.78

A3542 13 08 41.6 -34 34 28 15428 7 0 3.56

A3544 13 11 6.4 -32 59 34 15252 8 1 0.79

A3546 13 13 6.0 -29 58 46 9706 13 0 307+90−50 0.89 2.92 0.07

A3552 13 18 55.2 -31 49 4 15628 18 1 350+80−49 1.06 3.54 0.11

A3555 13 20 47.0 -28 58 48 14072 12 1 698+201−108 1.47 1.06 0.29

A3556 13 24 6.7 -31 40 10 14409 137 0 717+47−39 1.93 3.71 0.50

A3559 13 29 50.9 -29 30 51 14075 71 3 979+94−73 2.51 3.36 1.30

A3560 13 32 22.6 -33 8 22c 14672 69 3 742+73−56 1.53 1.06 0.33

A3564 13 34 20.8 -35 12 57 15220 26 1 572+102−67 1.68 3.52 0.42

A3566 13 38 58.0 -35 33 36 15460 44 2 483+62−45 1.08 0.99 0.13

A3568 13 41 13.9 -34 37 53 15550 18 1 675+154−92 1.88 3.75 0.52

A3570 13 46 52.5 -37 52 28c 11004 69 0 792+78−60 2.19 3.71 0.83

A3575 13 52 38.6 -32 53 16 11522 29 0 748+124−83 1.55 1.01 0.33

A3577 13 54 21.8 -27 50 11 14817 28 2 439+75−50 1.40 3.64 0.26

A3578 13 57 31.6 -24 44 21 11145 25 1 381+70−58 1.15 3.38 0.14

A3528N 12 54 22.1 -29 00 46a 16056 75 1030+96−75 1.36 0.13 0.24

A3528S 12 54 40.6 -29 13 44a 16215 49 1109+133−97 2.04 0.98 0.70

A3558 13 27 54.8 -31 29 32b 14257 126 4 1010+70−58 2.00 1.30 0.71

A3562 13 33 31.9 -31 39 37b 14508 62 2 1099+114−87 2.22 1.52 0.93

A3530 12 55 34.6 -30 20 9b 16291 47 0 755+92−68 1.53 1.07 0.34

A3532 12 57 22.1 -30 22 26b 16480 33 0 894+136−93 1.73 1.02 0.46

A3571 13 47 28.4 -32 50 59c 11702 58 2 1015+110−83 1.95 1.11 0.66

A3572 13 48 14.0 -33 22 56 15031 2 0 1.09

SC1327 13 29 45.4 -31 36 12b 14646 45 964+121−88 1.79 1.19 0.61

SC1329 13 31 36.0 -31 48 45b 13606 54 1060+120−89 1.95 0.50 0.53

(1) Name of cluster (A*** and S*** Abell et al. (1989).

(2,3) Equatorial J2000 centres, X-ray positions: a=Gastaldello et al. (2003), b=Breen et al. (1994),

c=Bohringer et al. (2004).

(4) Redshift.

(5) Number of cluster member redshifts used to find the mean cluster redshift.



70 Mpc.


(10) Cluster virial mass within an Abell radius (2.14 h−170 Mpc).


Figure 3.15: Colour magnitude plot for 4 supercluster clusters within the 2dFGRS region. Black

dots represent all SuperCosmos galaxies selected in the manner described in section 3.1.1, within

an Abell radius of the cluster centres. Blue crosses represent redshift selected cluster members.

The red line shows the adopted red sequence cut. (§3.2.1)

to the superclusters, all galaxies within the same extraction radii as for the radial

velocity calculations were extracted from the SuperCosmos Science archive (Hambly

et al., 2001). All galaxies had to be classified as a galaxy in each of the three bands

B, I and R2. In addition the quality of the detection had to be less than 128 in each

band and gCorMagB < 20.0 (magnitude if the object is assumed to be a galaxy).

UK Schmidt blue, Bj (B) and UK Schmidt red magnitudes (R2) were selected

for each galaxy. To remove background galaxies a colour magnitude cut was applied

to the the SuperCosmos samples. To obtain the cut, galaxies from four clusters

which had 2dFGRS redshifts available were overlayed on a colour magnitude plot

for all the SuperCosmos galaxies for the same clusters. The 2dFGRS galaxies were

only selected if they were within 3000 km s−1 of the mean cluster redshift and hence

were likely cluster members. From this overlay (see Fig. 3.15) a red sequence cut

was placed along the top of the redshift selected galaxies by eye. The line was found

to have a relation of bJ − rF = −0.15 bj + 4.3. The application of this cut to each

SuperCosmos sample left the likely members for each cluster for further analysis.

In order to obtain a profile of the optical surface brightness of the clusters we


required an analytical model which would fit the surface brightness curve of the

galaxies selected as cluster members. The models chosen did not have to be actual

optical surface brightness models, as long as their mathematical form fitted the

shape of our profiles. We selected four potential models which are described below.

The Navarro Frenk White Model

Navarro, Frenk & White (1996) used N-body simulations to investigate dark halos

in the Standard cold dark matter cosmology. They simulated the formation of 19

different systems with scales ranging from those of dwarf galaxies to those of rich

clusters. It was found that a model of the form shown in Eq. 3.4 provided a good fit

to the density profiles of four systems with a halo mass range of nearly four orders

of magnitude (Navarro, Frenk, & White, 1995).

ρ(r) =δc ρc

rrc

(

1 + rrc

)2 , (3.4)

where rc = r200/c is a characteristic radius, ρc = 3H20/8πG is the critical density (H0

is the current value of Hubble’s constant), and δc and c are two dimensionless pa-

rameters, representing the mean overdensity and central concentration of the radial

profile respectively.

The mass densities of the usual NFW profile are scaled to light density profiles

assuming light traces mass, at least in the visible cores of each cluster, such that

δλ = δc/Υ, where Υ ≡ M/L is the mean mass-to-light ratio of the cluster. This

results in the light profile,

λ(r) =δλ ρc

rrc

(

1 + rrc

)2 , (3.5)

where rc = r200/c is a characteristic radius, ρc = 3H20/8πG is the critical density (H0

is the current value of Hubble’s constant), and δc and c are two dimensionless pa-

rameters, representing the mean overdensity and central concentration of the radial

profile respectively. The two dimensional projected surface brightness of galaxies


on the sky can be computed by integrating Eq. 3.4 according to the Abell integral

equation given by,

Λ (R) = 2

∫ ∞

R

ρ (r)r√

r2 − R2dr (3.6)

Bartelmann (1996) show this results in the projected surface brightness of,

Λ (R) =2ρcδλrc

x2 − 1f(x), (3.7)

with

f(x) = 1 − 2√x2−1

arctan√

x−1x+1

(x > 1) (3.8)

f(x) = 1 − 2√1−x2 arctan

√

1−x1+x

(x < 1)

f(x) = 1 (x = 1),

where x = r/rc, R being the projected radius from the centre of the cluster.

The Hernquist Model

Hernquist (1990) presented a potential density pair which closely approximates the

de Vaucouleurs R1/4 law for elliptical galaxies. A modification of the distribution of

Jaffe (1983) allowed the intrinsic properties and projected distributions to be eval-

uated analytically,

ρ(r) =M

2π

a

r

1

(r + a)3, (3.9)

where M is the total mass and a is a scale length. So as to be able to apply this

form to our optical data, in the same manner as for the NFW profile, we divide

through by a constant mass to light ratio, Υ, obtaining the relation,

λ(r) =L

2π

a

r

1

(r + a)3, (3.10)


where L is the total light and a is a scale length. The two dimensional projected

surface brightness of galaxies on the sky can be computed by integrating Eq. 3.10

according to Eq. 3.6. This results in the projected surface brightness of,

Λ(R) =L

2πa2(1 − s2)2[(2 + s2) X(s) − 3], (3.11)

where s = R/a, R is the projected radius, L is the total light and

X(s) =1√

1 − s2sech−1s for (0≤s≤1) (3.12)

X(s) =1√

1 − s2sech−1s for (1≤s≤∞). (3.13)

The Plummer Model

The Plummer model was first used by Plummer (1911) to fit observations of globular

clusters and the density profile takes the form,

ρ(r) =3Mb2

4π

1

(b2 + r2)5/2, (3.14)

where M is the total mass of the cluster, and b is the Plummer radius, a scale pa-

rameter which sets the density of the cluster. In the same manner as the previous

models dividing by a constant mass to light ratio, Υ, results in the following light

profile,

λ(r) =3Lb2

4π

1

(b2 + r2)5/2, (3.15)

where L is the total light of the cluster. By integrating according to Eq. 3.6 the


projected surface brightness profile can be obtained as,

Λ(R) =L

π

b2

(b2 + R2)2(3.16)

The standard “beta” model

Traditionally models assume that the intra-cluster X-ray emitting gas is isothermal

and that the gas and the galaxies are in hydrostatic equilibrium. King (1962) pre-

sented an analytical approximation to the isothermal sphere which is often referred

to as the standard beta model. The surface X-ray brightness at projected distance

R is given by

Σ(R) = Σ0[1 + (R/rc)2]−3β+0.5, (3.17)

where rc is the core radius of the gas distribution and β is the ratio of the specific

energy in galaxies to the specific energy in the hot gas. We can simply apply this

to our optical data fitting optical surface brightness instead of X-ray, such that,

Λ(R) = Λ0[1 + (R/rc)2]−3β+0.5. (3.18)

Model choice

Each of the above projected models were fitted to the observed optical surface bright-

ness profiles obtained from the SuperCOSMOS galaxy data as described in §3.2.1,

using the Numerical Algorithm Groups (NAG) E04JYF algorithm. The models were

fitted with the following variables

1. Beta model: from Eq. 3.18, three variables were fitted, a=Λ0, b=β and c=rc.

2. Hernquist model: from Eq. 3.11 two variables were fitted, a=L and b=2πa2.

3. NFW model: from Eq. 3.7 two variables were fitted, a=rc and b=ρc δλ.

4. Plummer model: from Eq. 3.16 two variables were fitted, a=L and b=b.


Figure 3.16: Radial velocities of galaxies lying within the Abell radius of 2.14 h−1

70Mpc of each

galaxy cluster, belonging to the Pisces-Cetus supercluster, compiled from NED, 6dFGS, 2dFGRS

and SDSS. For each cluster, the mean recessional velocity is shown as a dotted line, and for those

with ≥12 redshifts, the velocity dispersion is shown on the upper right. (§3.2)



70Mpc of each

galaxy cluster, belonging to the Horologium-Reticulum supercluster, compiled from NED, 6dFGS,

(Fleenor et al., 2005) and (Fleenor et al., 2006). For each cluster, the mean recessional velocity is

shown as a dotted line, and for those with ≥8 redshifts, the velocity dispersion is shown on the

upper right. (§3.2)



70Mpc of each

galaxy cluster, belonging to the Shapley supercluster, compiled from NED, 6dFGS and ZCAT.

For each cluster, the mean recessional velocity is shown as a dotted line, and for those with ≥9

redshifts, the velocity dispersion is shown on the upper right. (§3.2)


Figure 3.19: Radial velocities of galaxies lying with an extraction radius of each galaxy cluster,

belonging to the Shapley supercluster. The extraction radii are shown in the top centre of each

cluster panel and are expressed as a fraction of the Abell radius ( 2.14 h−1

70Mpc). All clusters

belong to the Shapley supercluster and galaxies are compiled from NED, 6dFGS and ZCAT. For

each cluster, the mean recessional velocity is shown as a dotted line, and for those with ≥9 redshifts,

the velocity dispersion is shown on the upper right. (§3.2)

3.3. Virial mass estimates 69

An additional constant term to represent foreground/background galaxies was also

added as an extra +c term to all the models. For the majority of the clusters the

galaxies were binned in variable radius annuli around the cluster centre, such that

each annulus contains an equal number of galaxies. The luminosity per unit area in

each annulus was then calculated to plot the surface brightness profiles. However, a

satisfactory fit could not be found for some clusters using this method. Therefore,

for these profiles, equal radius annuli with a variable number of galaxies were used.

From this process the NFW model was seen to be the best overall model, fitting

the most cluster profiles accurately. Therefore, the NFW fit was used as the final

fit all of the clusters profiles to enable estimates of their mass to be performed.

The resulting surface brightness profiles and their associated NFW fits are shown

in Appendix A, Appendix B, and Appendix C for the clusters of the Pisces-Cetus,

Horologium-Reticulum and Shapley superclusters respectively.

3.3 Virial mass estimates

The mass within a radius r from the centre of a cluster can be derived from the

modelled velocity dispersion and spatial density profiles λ (r) (Koranyi & Geller,

2000). On assumption of a constant mass-to-light ratio Υ ≡ M/L, the mass density

ρ (r) ≡ Υ λ (r), following (3.4), results in the enclosed mass profile,

M(< r) = 4πδcρcr3c

[

ln(1 +r

rc) − r/rc

1 + r/rc

]

. (3.19)

The core radius rc has already been found in the fitting of the surface brightness

profile as described in §3.2.1. The quantity δc and c are linked by the requirement

that the mean density within r200 should be 200×ρc, i.e.,

δc =200

3

c3

[ln(1 + c) − c/(1 + c)], (3.20)

where c = r200/rc. With the value of rc already being calculated the NFW model

would be completely specified if we knew r200.

3.3. Virial mass estimates 70

From the definition of r200, we have that,

ρ200 = 200ρc, (3.21)

where ρ200 is the density inside r200 and ρc is the critical density of the universe.

This leads to,

M200 = 200 × 4πr3200ρc

3, (3.22)

where M200 is the mass inside r200. It can be shown that the critical density of the

universe can be expressed as,

ρc =3H2

0 (1 + z)3

8πG, (3.23)

where H0 is Hubble’s constant, G is the gravitational constant and z is the redshift.

Substituting Eq. 3.23 into Eq. 3.22 gives,

M200 =100r3

200H20 (1 + z)3

G(3.24)

It can be shown that the virial mass can be defined as,

Mv =3σ2rv

G, (3.25)

where rv is the virial radius. Dividing Eq. 3.24 by Eq. 3.25 gives,

M200rv

Mνr3200

= 100H20

(1 + z)3

3σ2r

, (3.26)

where σ2r is the radial velocity dispersion of the cluster and rv is the approximate

virial radius determined by

3.4. A lower limit to the Mass of the Superclusters 71

rv ∼ π

2

N(N − 1)∑

i

∑

i<j R−1ij

, (3.27)

where N is the number of galaxies in the system. The summation is over all pairs

of galaxies (i, j) within the Abell radius, where the projected separation for each

pair is Rij (Binney & Tremaine, 1987). This should provide a radius at which most

cluster members are included.

The enclosed mass profile (3.19) can be used to find M200 and Mν in terms of δc.

The calculated cluster masses within the Abell radius of 2.14 h−170 Mpc, their core

radii and virial radii found from the model fitting, can be found in Table 3.1,Table 3.2

and Table 3.3 for the Pisces-Cetus. Horologium-Reticulum and Shapley supercluster

clusters respectively.

The virial estimate will fail to represent the gravitating mass of a cluster which

is very obviously in the process of rapid evolution, e.g. a collapsing or interacting

system, since the virial theorem does not strictly apply to systems whose moment

of inertia is significantly changing with time. Abell 87 is obviously such a system

and hence its mass has been omitted.

3.4 A lower limit to the Mass of the Superclusters

The sum of the individual virial masses of the clusters, as calculated in the previous

section, can be treated as a lower limit to the mass of each supercluster.

3.4.1 Pisces-Cetus supercluster

For the filament containing A85, we use a cylindrical column of length equal to

the sum of the distances between the constituent clusters from the MST analysis

equalling 47.9 h−170 Mpc. Adopting a radius of 6 h−1

70 Mpc (Approximately 3 Abell

radii) gives a volume of 5421 h−370 Mpc3, we obtain the total mass of the clusters as

2.44× 1015 h−170 M⊙. As discussed in section 3.2 Abell 87 is likely to be a filament of

galaxies rather than a cluster and therefore its mass is not included.

3.4. A lower limit to the Mass of the Superclusters 72

For the filament containing A133, we use a cylindrical column of length of

167.8 h−170 Mpc again equal to the sum of the cluster separations form the MST anal-

ysis. The radius of 6 h−170 Mpc for the cylinder gives a volume of 18996 h−3

70 Mpc3,

we obtain the total mass of the clusters as 3.88 × 1015 h−170 M⊙.

With the critical density of the universe having a value of ρc = 1.36 × 1011 h270

M⊙ Mpc−3, these values for the mass of the Supercluster represent matter overdensi-

ties of δM ≡ ∆ρ/ρcrit >1.96 (over 5400 h−370 Mpc3) and δM >1.51 (over 19000 h−3

70 Mpc3)

for the A85-related and A133-related filaments respectively. Thus a mean for the

supercluster region of 1.74. These values are slightly lower than those found in the

core of the Shapley supercluster (5.2 over ∼ 22 h−1100 Mpc scale (Bardelli et al.,

2000)(extended sample)), (2.4 over ∼ 26 h−170 Mpc scale (Fabian, 1991)), (5.0 over

∼ 38 h−170 Mpc scale (Drinkwater et al., 2004)), (2.4 over ∼ 40 h−1

70 Mpc scale (Fleenor

et al., 2005)) and (5.4 over ∼ 30 − 46 h−170 Mpc scale (Proust et al., 2006)). The

cosmological significance of such overdensities in a supercluster filament has been

discussed in the literature (Raychaudhury, 1989; Ettori, Fabian, & White, 1997).

However, that these represent just the mass with some clusters omitted, no fila-

ment galaxies included, and that the matter density of the Universe is ΩM ∼ 0.3,

these amount to significant overdensities over very large volumes. This supports the

possibility that galaxies in these regions may evolve differently to galaxies which

are present in less dense regions and have different properties such as enhanced or

suppressed star formation.

3.4.2 Horologium-Reticulum supercluster

For the purposes of the estimate of a lower limit of the mass for the Horologium-

Reticulum supercluster we will take the super cluster to consist of those clusters that

are part of the main chain, joint by links of less than 20 h−1100 Mpc, represented by

solid lines in Fig. 3.8. The main chain spans from Abell 3089 through to Abell 3266,

containing 18 clusters (A3089, A3122, A3125, A3140, A3145, A3135, A3109, A3108,

A3100, A3123, A3120, A3110, A3078, A3074, A3125, A3158, A3164, A3225).

A lower limit of the mass of this structure found by summing all of the avail-

able masses of the constituent clusters results in a total mass of 6.60× 1015 h−170 M⊙.

3.5. Conclusions 73

Taking the volume of the supercluster to consist of a series of cylinders of radius

6 h−170 Mpc and length of the MST link between the clusters results in a total length

of 202.1 h−170 Mpc and a total volume of 22, 800 h−3

70 Mpc3. With the critical den-

sity of the universe having a value of ρc = 1.36 × 1011 h270 M⊙ Mpc−3, this value

for the mass of the Supercluster represents a matter overdensity of δM >2.1 (over

23, 000 h−370 Mpc3)

Again given that these represent just the mass with some clusters omitted, no

filament galaxies included, and that the matter density of the Universe is ΩM ∼0.3,

these amount to significant overdensities and the possibility of environmental effects

on the evolution of galaxies in the region.

3.4.3 Shapley supercluster

For the Shapley supercluster the main chain consisting of all clusters joined by

links of less than 20 h−1100 Mpc included all clusters accept for A1631, A1644 and

A1709. The total length of the MST links between these clusters was 195.31 giving

a volume of 22, 089 h−370 Mpc3 for the adopted cylinder radius of 6 h−1

70 Mpc. The

total mass is 1.2 × 1016 h−170 M⊙. With the critical density of the universe having a

value of ρc = 1.36× 1011 h270 M⊙ Mpc−3, this value for the mass of the Supercluster

represents a matter overdensity of δM >4.06 (over 22, 000 h−370 Mpc3).

This value is even higher than the previous two superclusters making the super-

cluster even more likely to effect the evolution of galaxies.

3.5 Conclusions

We have used survey redshifts (mainly from 2dFGRS, 6dFGS, SDSS, NED and

ZCAT) and photometry (from SuperCosmos) of galaxies belonging to the clusters

belonging to three superclusters to investigate its nature, extent and orientation.

The Pisces-Cetus supercluster consists of two main filaments, consisting of 11

and 5 clusters respectively, at mean redshifts of z =0.0625 and 0.0545 respectively.

The Horologium-Reticulum supercluster consists of 33 clusters of galaxies at a mean

redshift of z =0.0670 (MST maximum edge length = 25 h−1100 Mpc) and mainly

3.5. Conclusions 74

extends in the radial direction. Finally the Shapley supercluster consists of 29

clusters at a mean redshift of z =0.0476 MST maximum edge length = 25 h−1100 Mpc).

While there is some suggestion of filamentary structure in all three of the super-

clusters the position of the Pisces-Cetus supercluster with some coverage in both

the SDSS and 2dFGRS leads to the most compelling evidence. Most of chain A of

the Pisces-Cetus supercluster lies in the 2dFGRS region, and gives us a remarkable

three-dimensional view of a string of clusters, with groups delineating the filamen-

tary structure. Chain B, partially covered by the Sloan Digital sky survey, contains

the clusters A85 & A87, for which independent evidence exists (from X-ray obser-

vations) of collapse along the filament.

Virial masses were calculated from NFW fits to surface brightness profiles and

velocity dispersions for the constituent clusters, the sum of these masses being taken

as a lower limit to the mass of each of the superclusters. These were found to be

6.0 × 1015 h−170 M⊙ and 5.2 × 1015 h−1

70 M⊙ respectively for the chain A and chain B

of the Pisces-Cetus supercluster, 6.6 × 1015 h−170 M⊙ for Horologium-Reticulum and

1.2 × 1016 h−170 M⊙ for Shapley. These correspond to mass overdensities of δM >1.5,

δM >2.0, δM >2.1 and δM >4.1, for Pisces-Cetus chain A, Pisces-Cetus chain B,

Horologium-Reticulum and Shapley respectively.

These values indicate that in all three superclusters, it is likely that the systems

are just in the linear regime or have just left it. Furthermore, these overdensities

suggest that the regions may have different environmental conditions to other regions

and hence may have different effects on the evolution of galaxies.

Ever since the discovery of the “Great Wall”(Geller & Huchra, 1989), which

seemed to be a structure almost < 200 h−170 Mpc long, the discovery of comparable

structures have been claimed at higher redshift (e.g., Bagchi et al., 2002; Brand

et al., 2003; Miller et al., 2004). To be cosmologically significant, it is necessary

to show that these large structures are gravitationally bound, which is difficult to

demonstrate. In this work, we have found cluster filaments between approximately

50 h−170 Mpc and 130 h−1

70 Mpc long. This is consistent with statistical analyses of the

LCRS and 2dF redshift surveys, which indicate that the scale of homogeneity sets

in beyond the scale of ∼ 100 h−170 Mpc or so.

3.5. Conclusions 75

A limited X-ray analysis of the LX−σ relation in the clusters of the Pisces-Cetus

supercluster, based on literature X-ray data can be found in Appendix D.

Chapter 4

Benjamin Disraeli: “There are three kinds of lies: lies, damned lies, and statistics.”

Star formation in the Pisces-Cetus

supercluster

4.1 Introduction

Studies of the environmental effects on galaxy evolution in the past have shown that

star formation is suppressed in the cores of rich clusters (Dressler, 1980; Couch &

Sharples, 1987; Balogh et al., 1998). More recently, from the high-quality spectra

of the 2dFGRS and SDSS archives, the difference between the properties of star-

forming and quiescent galaxies have been further characterised, and shown to depend

on the local density of galaxies. For instance, studies (Lewis et al., 2002; Gomez et

al., 2003; Balogh et al., 2004) identifying star formation activity with the equivalent

width of the Hα emission line W (Hα), show that the fraction of galaxies with

W (Hα)>4 A steadily declines with increase in the local three-dimensional density

of galaxies. Kauffmann et al. (2004) show similar effects, with the star formation

history being quantified from line indices measured elsewhere in the spectrum as

well, including the Hδ absorption line and the strength of the 4000A break.

In the hierarchically merging scenario supported by large-volume numerical sim-

ulations such as Jenkins et al. (1998), much of this merger-driven evolution in the

history of a galaxy is expected to occur in small groups forming in and falling along

a supercluster filament towards regions of higher density. In the absence of direct

mergers, the close encounters between galaxies brought closer by dynamical friction,

76

4.2. Star formation within Pisces-Cetus supercluster filaments 77

can lead to galaxy harassment, which can also play a very important role in galaxy

evolution, and can affect the star formation properties of galaxies.

To investigate the star formation rate (SFR) within the galaxies that form the

Pisces-Cetus supercluster we use the 2dFGRS η parameter as discussed in Chapter

2.

4.2 Star formation within Pisces-Cetus superclus-

ter filaments

A supercluster filament is a snapshot of a cluster in formation, and the study of the

properties of galaxies as a function of position along a filament is expected to provide

insights into the processes involved in galactic evolution and cluster formation. This

section looks at galaxies in a few filaments of the Pisces-Cetus supercluster.

The clusters comprising the Pisces-Cetus supercluster, taken from the minimal

spanning tree (MST) analysis of Raychaudhury et al. (2007), form the core of our

sample. The filamentary nature of the region can clearly be seen in the distribution

of galaxies in the groups in Fig. 4.2, where the 2dFGRS galaxies within 1840 kms−1

(three times the velocity dispersion of the clusters belonging to the supercluster),

are plotted. The 2PIGG groups found within the same velocity bounds (Eke et al.,

2004), also show the same large-scale structure. The rich clusters, plotted as large

circles on the same plot, can be seen to be mostly along these filaments forming the

supercluster structure.

4.2.1 Filament membership

Our sample of galaxies was taken from the 2PIGG (Eke et al., 2004) subsample of

the 2dFGRS comprising 191,328 galaxies. This leaves out about 20 % of galaxies

in the parent sample in under-sampled regions and ensures a uniform completeness

limit all over the survey. This enables comparisons with 2PIGG statistics to be

made without bias. Hereafter, 2dFGRS refers to this subsample.

From this subsample, galaxies which belong to the three most prominent fila-


Figure 4.1: (a, Left) All 2dFGRS Galaxies within 1840 km s−1 (3σ) of the mean recessional

velocity of the Pisces-Cetus supercluster. The filamentary structure is clearly visible. (§4.2)

Figure 4.2: Clusters of galaxies belonging to Pisces-Cetus supercluster filaments within the

2dFGRS region and within 1840 km s−1 (3σ) of the mean supercluster velocity. The largest circles

represent Abell clusters, and the medium-sized ones are supplementary Abell and Edinburgh-

Durham clusters within the same redshift range. The groups of galaxies (Eke et al., 2004, 2PIGG)

within the same velocity bounds, identified from a friends-of-friends analysis of the 2dFGRS are

shown as the smallest circles. (§4.2)


Figure 4.3: The 2dFGRS galaxies that form the three filaments as defined in the text are shown

as crosses. All galaxies within the 2dFGRS in the region are shown as dots. (§4.2.1)

ments, longer than 20 h−170 Mpc, seen in Fig. 4.2, namely those joining A2800-A2734,

A2734-E0365 and E0365-A2716, were extracted.

We define the extent of each filament as an prolate spheroid, with the centres of

the two clusters involved being at each end, the distance between them being the

major axis of the spheroid, and 6 h−170 Mpc being the semi-minor axis. All galaxies

falling inside this spheroid were taken to be members of the filament. So as to not

omit cluster galaxies at each end of the filament, we added the galaxies found, from

a percolation analysis, to belong to the corresponding 2PIGG “group” in (Eke et al.,

2004). The resulting 965 filament members can be seen in Fig. 4.3.

The distance between two clusters, and between a galaxy and a cluster, was

calculated as the co-moving proper distance between them (see Hogg, 1999). We

used the measured redshift of each galaxy as a measure of its distance from us,

except if it is a member of a rich cluster, where the mean redshift of the cluster was

used.

Fig 4.2.1 shows the distribution of the 2dFGRS galaxies for the 2PIGG group

corresponding to Abell 2734. The red circle in the left hand plot shows the Abell

radius (2.14 Mpc h−170 ). This demonstrates that simply taking cluster members to


Figure 4.4: The distribution of the 2dFGRS galaxies for the 2PIGG group corresponding to

Abell 2734. (left) Distribution in R.A.-Dec. space with the Abell radius (2.14 h−1

70Mpc) shown

as a red circle. (top, right) Distribution in redshift-Dec. space, where the centre of the cluster is

shown as a blue circle. Dot-dash lines show 1000 km s−1 increments of redshift from the mean

cluster redshift. (bottom, right) Distribution in redshift-R.A. space , the centre of the cluster is

shown as a blue circle, dot-dash lines show 1000 km s−1 increments of redshift from the mean

cluster redshift. (§4.2.1)

be within the Abell radius would omit some cluster members.

4.2.2 Star formation along the A2734-A2800 filament

We start our exercise by looking in detail at the most prominent filaments in the

Pisces-Cetus supercluster, that linking A2734 and A2800, which is about 32 h−170 Mpc

long. The co-moving distance of each of the filament galaxies from one end (A2734)

was calculated as described above. Members of A2800 were assigned a distance

equal to the separation of the two clusters minus their projected distance from the

centre of A2800.

Along the filament, we chose bins of varying size according to the numbers

of galaxies available. Closer to the two clusters, we chose smaller bins of 0.3 −


Figure 4.5: For the filament of galaxies linking A2734 and A2800, the mean η is plotted as a

function of the distance from the centre of A2734. The “field” value, the mean η for all galaxies of

the 2dFGRS, is around zero. The bottom panel shows the fraction of passive galaxies (η <−1.4)

in each bin. It can be seen, as expected, that the SFR is lowest at the cores of the two rich

clusters, where the number of passive galaxies is the highest. The mean η seems to peak between

3–4 h−1

70Mpc from each end. (§4.2.2)

0.6 h−170 Mpc to sample the rapid variation of SFR within the virial radius of the

cluster. For each bin, the the mean distance of all member galaxies, and the mean

η, were calculated.

Fig. 4.5 shows the resulting plot of mean η as a function of distance from A2734.

We also plot, in the bottom panel, the fraction of passive (η<−1.4) galaxies in each

bin. It can be seen, as expected, that the SFR is minimum at the cores of the two

rich clusters, where the number of passive galaxies is the highest. The mean value

of the η parameter increasing with distance to approximately the field value (the

mean η for all galaxies of the 2dFGRS is around zero).

However, it can also be seen that between 3–4 h−170 Mpc from the centre of A2734

there is a peak in the mean η. There is another peak at the A2800 end of the plot

at a slightly closer distance from the cluster centre. Although within errors one of

them does not rise above the field, there is enough of an indication of a peak to

warrant further investigation by increasing numbers. To investigate the reality of

the signal, we will now stack all three filaments in our sample, and fold Fig. 4.5 such


Figure 4.6: The distribution of passive (η<−1.4) galaxies shown as filled circles and star forming

(η>−1.4) galaxies shown as crosses in the region surrounding Abell 2800. Only galaxies belonging

to the A2734–A2800 filament are shown. The concentric circles are at 1 h−1

70Mpc intervals. (§4.2.2)

that we consider distances along the filament from the nearest cluster.

Fig. 4.6 and Fig. 4.7 show the distribution of the passive and star forming galaxies

for Abell 2800 and Abell 2734 respectively. The concentric circles are at 1 h−170 Mpc

intervals and it can be seen that in the 3–4 h−170 Mpc annulus there are more star

forming than passive galaxies for both clusters.

4.2.3 Star formation properties of galaxies in all three fila-

ments combined

The distance of each of the filament members from the nearest of the two clusters

at either end was calculated using the same method as above.

Here we combine the three filaments longer than 20 h−170 Mpc, namely those

joining A2800–A2734, A2734–E0365 and E0365–A2716, seen in Fig. 4.3. All galaxies

belonging to the three filaments were grouped in bins of varying size according to

their distance from the nearest cluster (representing the extremities of the filaments).

As above, we plot the mean value of η and the fraction of passive galaxies in each

bin in Fig. 4.8. For comparison between the trend with distance for the filament

galaxies with galaxies elsewhere, we compute “field” values from the whole 2dFGRS,


Figure 4.7: The distribution of passive (η<−1.4) galaxies shown as filled circles and star forming

(η>−1.4) galaxies shown as crosses in the region surrounding Abell 2734. Only galaxies belonging

to the A2734–A2800 filament are shown. The concentric circles are at 1 h−1

70Mpc intervals. (§4.2.2)

Table 4.1: Virial radii for Pisces-Cetus filament clusters

Cluster σ Virial radius

(kms−1) (Mpc)

A2800 567 1.62

A2734 848 2.42

A2716 812 2.32

E0365 442 1.26

where distances are calculated from the nearest 2PIGG group of ≥ 30 members (the

equivalent of a rich cluster), shown as the dashed line.

While the “field” values of mean η increase steadily with distance from the centre

of the nearest cluster, the galaxies in the filaments, binned in the same way, show a

peak between 3–4 h−170 Mpc, confirming our finding from the single filament above.

A rough estimate of the virial radius of each of the clusters is calculated using

the formula of Girardi et al. (1998), Rv = 0.002σ(h−1Mpc), where σ is the one-

dimensional velocity dispersion. These are shown in Table 4.1.

The peak region therefore corresponds to about 2 virial radii. A corresponding

dip in the percentage of passive galaxies is also seen at this distance. Of course, star


Figure 4.8: (a, Top) For the three filaments combined, the mean η as function of distance from

the nearest cluster is shown. The dashed line shows the mean η as function of distance from the

nearest 2PIGG group with ≥ 30 members for all 2dFGRS galaxies. (b, Bottom) For the same

galaxies as above, the fraction of these galaxies with an η<−1.4 is shown as a function of distance

from the nearest cluster. The dashed line showing the same fraction as a function of distance from

the nearest 2PIGG group with ≥ 30 members for the whole 2dFGRS. (§4.2.3)

formation is suppressed as the galaxy approaches the core of the cluster, leading to

a low mean η and a higher fraction of passive galaxies interior to this distance. The

cause of the enhanced star formation is discussed in more detail in (§4.3).

To get a better picture of how the values of η for the individual galaxies contribute

to the means, a histogram of η in each of the 8 bins is shown in Fig. 4.9. It can be

seen that the large peak of galaxies at the lowest levels of SFR seen in the first three

bins is missing in bins 5 and 6. This combines with a relatively high percentage of

galaxies having high η values of above 0 is consistent with the corresponding peak

in the mean η of Fig. 4.8.

4.2.4 Star formation in high and low velocity dispersion

clusters

If tidal forces were an important influence on the peak in star formation, we would

expect that the position of any region of enhanced star formation would vary ac-


Figure 4.9: For the three filaments combined, histograms of the galaxy η’s in each of the 8

distance bins. (§4.2.3)

cording to the velocity dispersion of the cluster that it was nearest to. Tidal forces

are proportional to M/R3, where M is the mass of the cluster and R the distance

from the cluster at which tidal forces are encountered. Since the mass of a cluster is

proportional to σ2Rv, where σ is the velocity dispersion, you would expect galaxies

falling into clusters of larger velocity dispersion to encounter tidal forces at larger

distances.

We therefore split the four clusters that form our filaments into those with high

velocity dispersions (A2716 = 812 km s−1, A2734 = 848 km s−1) and those with low

velocity dispersions (A2800 = 567 km s−1, E0365 = 426 km s−1). Distances from

the clusters in each of the two samples were then calculated for the galaxies from

the three filaments. Fig. 4.10 shows the resulting values for mean η as a function

of distance for the high and low velocity dispersion cluster samples. It can be seen

that there is no significant difference in the position of the low velocity dispersion

cluster peak in mean η (filled circles) and the peak in the high velocity dispersion

cluster peak (open circles).


Figure 4.10: (a, Top) For the three filaments combined, the mean η as function of distance from

the nearest high or low velocity dispersion cluster is shown. Distances from low velocity dispersion

clusters (A2800 and E0365) are shown as filled circles, while distances from high velocity dispersion

clusters (A2734 and A2716) are shown as open circles. The dashed line shows the mean η as

function of distance from the nearest 2PIGG group with ≥ 30 members for all 2dFGRS galaxies.

(b, Bottom) For the same galaxies as above, the fraction of these galaxies with an η<−1.4 is shown

as a function of distance from the nearest cluster. The dashed line showing the same fraction as

a function of distance from the nearest 2PIGG group with ≥ 30 members for the whole 2dFGRS.

(§4.2.4)


Figure 4.11: Star formation in giant galaxies (MB ≤−20) vs that in dwarfs (−20<MB≤−17.5),

in the three filaments combined. (a, Top) The mean star formation rate parameter η is shown as

function of distance from the nearest cluster, for dwarfs (open triangles) and giants (filled circles).

(b, Bottom) The fraction of these galaxies with η <−1.4 is shown as a function of distance from

the nearest cluster. (§4.2.5)

4.2.5 Star formation in giant and dwarf galaxies

As samples of galaxies with estimated star formation properties grow larger, it would

become easier to study the relation between star formation in a galaxy and various

properties of its environment, and those of the galaxies themselves (e.g., Haines et

al., 2006a).

Here, in Fig. 4.11, we break up the galaxies plotted above in Fig. 4.8 into two

subsamples: giant galaxies (MB ≤−20) and dwarf galaxies (−20<MB ≤−17.5). As

a result there are are 119 giants and 846 dwarfs in the three filaments used above.

As in Fig. 4.8, we plot the mean value of η as a measure of star formation, and the

fraction of passive galaxies, as a function of their distance from the nearest cluster,

with dwarfs plotted as open triangles and giants as filled circles.

It seems that the peak in mean η seen in Fig. 4.8, between 3 − 4 h−170 Mpc, is

almost entirely due to enhanced star formation in dwarfs, indeed there are no passive

dwarf galaxies in the bin containing the peak in mean η.

It can be seen in Fig. 4.12, especially for the giant galaxies that there are more


Figure 4.12: The distribution of giant (MB ≤−20) and dwarf (−20 < MB ≤−17.5) galaxies,

in the three filaments combined in R.A.-Dec. space. Also shown is the current star formation of

these galaxies with passive (η <−1.4) galaxies shown as blue and star forming (η <−1.4) as red.

The green circles show the virial radius of each cluster. (§4.2.5)

passive galaxies within the virial radius than star forming. The virial radii are taken

from Table 4.1.

While the differences in the populations would appear to be real it is worth re-

membering that the populations were determined from the blue magnitudes. The

blue magnitude will be boosted by star formation and therefore the high η galaxies

will have preferentially higher blue magnitudes, This will result in some dwarf galax-

ies being shifted into the giant population. This might explain why our populations

overlap at lower radii unlike the completely separate lines of Haines et al. (2006a)

who use SDSS R band data. Ideally K-band magnitudes would have been used to

separate our populations, but we do not have such magnitudes available from the

2MASS survey for all our galaxies.

4.2.6 Star formation in Groups

The suppression of star formation with increasing local density of galaxies has been

observed to occur in giant galaxies at very low values of the local projected density

(∼ 1 h−170 Mpc−2) (e.g. Lewis et al., 2002; Gomez et al., 2003), which are typical

of densities well-outside the virialised regions in clusters, indicating that the cause


does not lie entirely in the influence of the cluster environment. One suggestion

is that much of the evolution of galaxies occurs in groups during their life on the

filaments, before the groups are assimilated in clusters. Evidence supporting this

is found in the virialised structure of some galaxy groups (O’Sullivan, Forbes, &

Ponman, 2001). If so, the trend seen in the previous section would be different for

filament galaxies that belong to groups and those that are relatively isolated.

We divide our sample of galaxies that are members of the three Pisces-Cetus

filaments into those that belong to groups (2PIGG groups with 4 or more mem-

bers, (Eke et al., 2004), and relatively isolated galaxies, which are galaxies that are

not members of 2PIGG groups. Fig. 4.13 shows the variation of mean η and the

fraction of passive galaxies for these two subsamples, as a function of the distance

from the nearest cluster for the filament galaxies. There is a large scatter in the

points corresponding to non-group galaxies (representing only 8% of the total num-

ber in the sample). There is very weak evidence that the peak in mean η occurs in

groups at smaller distances than in the non-group galaxies, which in general have a

higher fraction of star forming galaxies. However, as non-group galaxies can not be

found within approximately 3 h−170 Mpc of the cluster centres there will be a consid-

erable selection bias against having a peak in star-formation in non-group galaxies

at 3 h−170 Mpc or less.

Fig. 4.14 compares the same quantities for galaxies that belong to groups (2PIGG,

N ≥4) in these three filaments to similar group galaxies elsewhere in the 2dFGRS.

The black dots represent the variation of mean η and passive galaxy fraction as a

function of distance from the nearest cluster in the 2dFGRS. The plots suggest that

in the sample representing the whole 2dFGRS the SFR is more or less uniform in

all group galaxies irrespective of their distance from the nearest cluster, except for

those galaxies within the virial radii of clusters. In sharp contrast, the trend we find

of a peak in SFR between 3 − 4 h−170 Mpc is seen in the group galaxies that belong

to filaments.

To investigate whether the groups that we were comparing the SFR in were the

same basic entities in the three filaments and in the whole 2dFGRS, we have plotted

histograms of the richness and velocity dispersion for these group samples. These


Figure 4.13: (a, Top) The mean value of the η as a function of distance from the nearest

cluster, for all galaxies in the three filaments combined. Galaxies that are members of groups

(2PIGG groups with N ≥ 4) are shown as filled circles while galaxies that are not part of a group

as squares. (b, Bottom) The fraction of filament galaxies with η<−1.4 is plotted as a function of

distance from the nearest cluster for the same samples. (§4.2.6)

Figure 4.14: Star formation in galaxies in 2dFGRS groups: those in filaments vs the entire

2dFGRS: (a, Top) The mean value of the η as a function of distance from the nearest cluster.

Filament galaxies that are members of groups (2PIGG groups with N ≥ 4) are shown as crosses.

This is compared to a sample of ALL galaxies in the 2dFGRS that are members of similar 2PIGG

groups (dashed line). The peak in η is not seen in the latter category. (b, Bottom) The fraction

of filament galaxies with η <−1.4 as a function of distance from the nearest cluster for the same

samples. (§4.2.6)


Figure 4.15: (a, Left) Histograms of the relative number of groups with richness 0-25 for

groups (2PIGG groups with N ≥ 4) within the 3 filaments of the Pisces-Cetus supercluster (green)

and groups within the entire 2dFGRS (Red). (b, Right) Histograms of the relative number of

groups with velocity dispersion 0-1000 Kms−1 for groups within the 3 filaments of the Pisces-

Cetus supercluster (green) and groups within the entire 2dFGRS (Red). (§4.2.6)

histograms can be seen in Fig 4.15a and Fig 4.15b. It can be seen that there is some

evidence that the group galaxies in the filaments (green histograms) have richer

groups. There is also marginal evidence that the group galaxies in the filaments

have larger velocity dispersions in the range up to 400 kms−1. This may be due

to the filamentary structure of the region causing the percolation algorithm used in

finding the groups to include more group members and hence the groups to have

larger velocity dispersions. Due to this effect and the marginal results of our group

work we have chosen not to emphasise the group results.

4.2.7 Welch’s test results

Given two data sets, each characterised by its mean, standard deviation and number

of data points, we can use some kind of t test to determine whether the means are

distinct, provided that the underlying distributions can be assumed to be normal.

All such tests are usually called Student’s t tests, though strictly speaking that

name should only be used if the variances of the two populations are also assumed

to be equal. In our case the variances of our means do not have the same variance

and so we use a variant of the Student’s t tests, Welch’s t test. Welch’s t test is

an adaptation of Student’s t-test intended for use with two samples having unequal


Table 4.2: Welch’s test results for Pisces-Cetus filamentsFigure Probability

number 1 2 3 4 5 6 7 8 9 Joint (4-9)

Fig. 4.8 7.6E-5 2.4E-3 0.53 0.93 0.14 0.74 0.83 0.36 0.42 0.01

Fig. 4.10 ∗ 5.2E-5 0.027 0.006 0.004 0.83 0.28 0.25 0.93 0.67 1.4E-4

Fig. 4.11 0.57 0.89 0.72 0.02 0.0076 4.4E-6 0.17 0.001 1.14E-13

Fig. 4.13 0.71 0.46 0.20 0.16 0.01

Fig. 4.14 3.1E-7 3.1E-5 0.53 0.61 0.28 0.38 0.04 0.77 0.74 1.4E-3

(*) Note that in the case of Fig. 4.10, the test is performed between the low and high velocity dispersion samples,

represented by the filled and open circles respectively.

variances, with the statistic given by,

t =Xa − Xb

[var(Xa)/Na + var(Xb)/Nb]1/2, (4.1)

where Xa is the mean value in dataset 1, Xb is the mean value in dataset 2, var(Xa)

is the variance of dataset 1, var(Xb) is the variance of dataset 2, Na is the number

of data in datset 1 and Nb is the number of data in datset 2. The number of degrees

of freedom, v, is given by,

vXa−Xb=

[

var(Xa)Na

+ var(Xb)Nb

]2

[var(Xa)/Na]2

Na−1+ [var(Xb)/Nb]2

Nb−1

, (4.2)

The above formulas as part of the “tutest” routine from Press et al. (1992) were

applied to the mean η in each bin of our SFR as a function of distance from the

centre of a cluster and gave the results seen in Table 4.2. The joint probability

for the filament region outside of the cluster radius (bins 4-9) is also shown in

Table 4.2. It can be seen that for Fig. 4.8 the point at which the SFR of the filament

galaxies peaks, has a probability of 0.14 of the means being equal. This corresponds

approximately to a 1.5 σ result, which while not overwhelmingly significant, the

result persisted in various subsets of the Pisces-Cetus sample, i.e. the filaments

taken independently, as well as the high and low velocity dispersion cluster samples.

With the sample drawn from the entire 2dFGRS having no such result this suggests

that the result may be stronger than that which the statistics show. The first 4 bins

of Fig. 4.10 show significant differences between the high and low velocity dispersion

clusters (see §4.3) with three of the bins having probabilities of approximately 3 σ

4.3. Discussion 93

or greater. The joint probabilities shows that the populations that are the most

different to each other are the dwarf and giant samples of Fig. 4.11.

4.3 Discussion

The most striking of our results are those seen in Fig. 4.8, where we look at galaxies

which are members of filaments joining pairs of rich clusters of galaxies. We see a

decline in SFR in these galaxies, from the filament environment on the periphery of a

cluster, to the galaxies in the cluster core, that indicate a physical mechanism at work

that quenches star formation progressively as a galaxy approaches the core of the

cluster potential well. This trend is consistent with that seen in other environmental

studies (e.g., Balogh et al., 1998; Moran et al., 2005). However the unusual feature

in our own case is that, on top of this decline we see a nearly instantaneous effect

which causes a burst of star formation at ∼ 3 h−170 Mpc from its centre, which is

about 1.5–2 times the virial radius of the cluster.

It has been shown that galaxies can be surrounded by a halo of hot gas with

a temperature of up to a few million degrees Kelvin (e.g., Pedersen et al., 2006).

However, it is likely that many more galaxies have a warm halo of gas with a

temperature of a few hundred thousand degrees Kelvin which is too cool to be seen

in X-ray detections and too warm to be seen in radio detections. This halo of

warm gas would provide a store of gas which can be used as fuel for continued star

formation in galaxies.

As galaxies approach the gravitational potential well of cluster, they will start to

encounter the Intracluster Medium (ICM), possibly at a distance much larger than

the virial radius. Approaching the outer regions of the cluster along a filament,

at the same time, the density of galaxies will begin to increase rapidly. At this

stage the galaxies will start to lose their warm gas haloes through evaporation and

possibly ram pressure stripping, as the gaseous halo of the galaxy interacts with the

hot ICM. This will lead to a steep decline in the SFR of galaxies between about

∼ 3 h−170 Mpc, progressively to the centre. This is seen in Fig. 4.8. When the galaxies

reach the very dense core region of the clusters at < 1 h−170 Mpc, galaxy harassment

4.3. Discussion 94

(Moore et al., 1999) will become an important effect. With a lot of their gas already

removed by this stage, star formation will not be induced by the harassment, and

the remaining gas of the galaxy will now be stripped, leading to the observed steep

dip in SFR in the first two bins from the centre of the cluster.

Superposed on this trend, a rapidly acting process such as galaxies experiencing

the ICM for the first time or galaxy harassment are the most likely candidates for

our observed sudden burst in SFR at ∼ 3 h−170 Mpc from the cluster. As galaxies

just start to encounter the ICM they will not yet have had their gas stripped or

evaporated, but the interaction with the ICM will lead to shocks leading to a burst

of star formation. Similarly, with their gas still intact, galaxy harassment may lead

to density fluctuations in the gas which may trigger a burst of star formation. In

the infall region of the cluster at a few h−170 Mpc, the galaxies will just have started

to encounter the density of galaxies needed for galaxy harassment to become an

important factor. The sharpness of the peak in SFR is another indicator that galaxy

harassment may be important, since Moore et al. (1999) show that harassment is a

rapid effect.

The effects of “backsplash” (Gill, Knebe, & Gibson, 2005) which are strongest in

approximately the 1− 2 h−170 Mpc range are not likely to have a strong effect on our

peak in SFR, which is further out, but it may mean that the increase in SFR in some

galaxies in the sharp peak region may be even stronger than our mean suggests.

Moran et al. (2005) also observe a peak in SFR in the approach to the rich cluster

CL0024 at z=0.4. Their peak however is observed at 1.8 h−170 Mpc, i.e. at approxi-

mately half the distance of our peak. It is possible the discrepancy between the two

may stem from the fact that we are looking at galaxies falling into clusters along

filaments. In the case of CL0024, galaxies are falling into the cluster isotropically,

while ours are falling in along a denser filament of galaxies, which can lead to a

higher local density. This may lead to our galaxies encountering galaxy harassment

further from the cluster core.

Our peak in SFR may even contribute to our steep gradient within ∼ 3 h−170 Mpc,

making it steeper. The galaxies that are star forming will have had their gas tem-

perature raised and thus when they encounter the ICM they will be more prone to

4.3. Discussion 95

evaporation and stripping and hence have a rapidly decreasing SFR (for a similar

effect on groups see Rasmussen, Ponman, & Mulchaey, 2006).

The principal component analysis used in obtaining the η parameter will not

have removed contributions from active galactic nuclei (AGN). It therefore remains a

possibility that our peak in SFR is due to AGN activity rather than conventional star

formation. In fact this would be fairly consistent with the X-ray results of Ruderman

& Ebeling (2005) who find a prominent spike in the number of cluster AGN at

∼ 2.5 h−170 Mpc. However, the detection of X-ray AGN does not necessarily confirm

the presence of an optical AGN (Shen et al., 2007) and the above arguments are more

suggestive of galaxy harassment being the dominant effect leading to starbursts.

Fig. 4.10 shows that there is no real difference in the position of the peak in SFR

in the infall regions of high or low velocity dispersion clusters. Therefore, either

the enhanced star formation that we are seeing is not due to the tidal effects of

the cluster or the tidal forces are being masked by stronger effects such as those

described above. However this plot does show a marked difference between the low

and high velocity dispersion distributions in the first 4 bins. In this region the high

velocity dispersion clusters are at significantly lower SFRs, this is consistent with

the higher velocities resulting in more ram pressure stripping and hence there is less

gas available for star formation.

Fig. 4.11 shows that our dwarf galaxies generally have a higher SFR than the

giant galaxies. This is consistent with the results of Haines et al. (2006a) and

Moran et al. (2005). This also provides more evidence for galaxy harassment being

the dominant influence on the burst in star formation, dwarf galaxies are expected

to be more vulnerable to galaxy harassment than giants. Moran et al. (2005) shows

this, where almost all the galaxies in their peak in the [OII] equivalent width are

dwarfs.

The fact that our peak in SFR is mainly due to the dwarf galaxies also means

that the burst in SFR is unlikely to be due to merging of galaxies. The small merger

cross sections of dwarfs make them unlikely candidates for mergers.

Fig. 4.13 suggests that non group galaxies may have higher SFR at greater

distances from the cluster core. However, the low numbers of galaxies used here

4.4. Conclusions 96

make the trend inconclusive. This will be investigated with a larger sample of

galaxies in Chapter 5.

4.4 Conclusions

We investigated the environmental dependence of star formation within a superclus-

ter environment. We have done this by finding the variation of the η parameter with

distance from cluster centres along filaments of galaxies joining rich clusters.

For galaxies belonging to three filaments (each over 20 h−170 Mpc long), connecting

three pairs of rich clusters, we have looked at the variation of the mean η parameter

with distance along the filaments, in bins of one to a few h−170 Mpc, starting from the

cores of the rich clusters out to the sparser reaches of the filament. We have also

looked at similar dependence on distance of the fraction of passive galaxies (η<−1.4,

which is equivalent to the equivalent width of the Hα emission being less than 4 A),

in each distance bin. In doing so, we have also noted whether these galaxies are

giant (MB ≤−20) or a dwarf, or member of a group or a cluster. Where possible, we

have compared these results to similar properties of galaxies elsewhere in the 2dF

galaxy redshift survey.

It is well known that in the cores of rich clusters, the star formation rate in a

galaxy is very low, irrespective of its mass, and and this we confirm by showing

that the value of mean η and the fraction of passive galaxies falls to its lowest value

for both giant and dwarf galaxies in the cores of clusters, both in the supercluster

filaments as well as elsewhere in the 2dFGRS. As one moves away from the cores of

clusters along the filaments, there is an increased activity of star formation, peaking

in the range 3 − 4 h−170 Mpc, which is 1.5–2 times the virial radius of the clusters.

This peak in star formation in filament galaxies is seen to be entirely due to dwarf

galaxies (−20<MB ≤−17.5). More luminous galaxies (MB ≤−20) have much lower

star formation in general in agreement with previous work done by others.

We have also examined the influence of the group environment on the SFR in

the galaxies within the filament. There is some evidence to suggest that the peaks

in mean η are present in more or less the same position in both group and non-group

4.4. Conclusions 97

galaxies. It is also seen that there is little variation in mean η with distance for the

group galaxies taken from the whole 2dFGRS. This is in contrast with the group

galaxies within the filaments which again show a peak at approximately 3 h−170 Mpc.

This would suggest that the filament environment is dominant over the group envi-

ronment with respects to SFR at this distance.

The possible physical mechanisms for the gradient in SFR and the peak in SFR

at ∼ 3 h−170 Mpc have been discussed in §4.3 and galaxy harassment is seen as the

most likely candidate for the rapid burst in star formation.

Finally, although these results in this work are indicative of interesting envi-

ronmental effects on star formation in galaxies, investigated at a level beyond the

usual projected local densities that are more commonly found in the literature, they

come from a small sample of about a thousand galaxies in three filaments in a single

supercluster. Moreover, we have used an indirect measure for star formation (the

η parameter) in these galaxies. It would therefore be useful to explore these effects

in a large ensemble of filaments from both the 2dFGRS and 6dFGRS, not only us-

ing various measures of star formation, but also scrutinising the effects of various

environmental parameters that large samples can afford.

Chapter 5

The 1st Duke of Wellington: “Wise people learn when they can; fools learn when

they must.”

Star formation in 2dFGRS

filaments

5.1 Introduction

In Chapter 4 we investigated the environmental dependence of star formation within

three filaments joining rich clusters of the Pisces-Cetus supercluster region. We

observed that as one moves away from the cluster cores there is an increased activity

of star formation, with a peak in the 3-4 h−170 Mpc range along the filaments over

and above the gradual increase in star formation rate (SFR) away from the cluster

cores. While this is a striking result, these results come only from approximately

1,000 galaxies in three filaments, and in one supercluster. To confirm that the

observed effect is not confined to this one supercluster, a larger sample of filaments

is therefore required. Since the Pisces-Cetus supercluster is the only supercluster

of the Raychaudhury et al. (2007) catalogue within the 2dFGRS region, we sought

another source of filaments.

In this Chapter, we have drawn from the filament catalogue of Pimbblet, Drinkwa-

ter, & Hawkrigg (2004) which listed 805 “filaments” identified among the galaxies

of the 2dFGRS, this sample will be referred to as the PIM04 sample. Since the

catalogue is compiled from the 2dFGRS, the η parameter was once again available

as an estimator of star formation for all the member galaxies.

98

5.2. The filament catalogue 99

5.2 The filament catalogue

The source catalogue of potential filaments was composed from the cluster catalogue

of De Propris et al. (2002) consisting of over 800 cross correlations with the Abell

(Abell et al., 1989), the Edinburgh Durham Cluster Catalogue (Lumsden et al., 1992)

and the APM survey cluster catalogue (Dalton et al., 1997). From this catalogue,

they select potential intercluster filaments, by applying the following criteria:

1. The clusters must be spatially close, < 10 degrees on the sky. At a median

redshift of z = 0.1, this corresponds to a projected length of ≈ 45h−1 Mpc.

2. Their recession velocities must not differ by more than z = 1000 km s−1.

3. Clusters common to the Abell, EDCC and APMCC catalogues are removed

to prevent self-pairing. This resulted in 805 unique potential intercluster fila-

ments.

Based on the method of Colberg, Krughoff, & Connolly (2005) the potential

filaments are then classified into types. This is done by drawing a vector from one

cluster centre to the other and then extracting all galaxies within 20 h−1100 Mpc of this

axis with a depth of 5 h−1100 Mpc. These galaxies are then placed onto two orthogonal

planes containing the intercluster axis and smoothed with a circular top-hat function

of radius 1 h−1100 Mpc. The two projections were then visually inspected and classified

according to Table 5.1.

5.3 The samples

5.3.1 Filament selection

Further criteria were applied to narrow down the initial sample of 805 potential fila-

ments. Only filaments having a length of between 10 and 40 h−170 Mpc were selected.

Further more, potential filaments that had a classification (see Table 5.1) of “near

coincidental clusters” or “Nil” were also removed. This resulted in a sample of 432

filaments to study visually. Each of the 432 filaments had two clusters from which

Pimbblet, Drinkwater, & Hawkrigg (2004) had identified a filament. In addition

5.3. The samples 100

Table 5.1: Filament type classification in the PIM04 sample

Type Filament description

Nil No filament is detected.

0 Near-coincident clusters. The cluster pair overlaps to such a degree that

any filament present cannot be isolated.

1 Straight. The filament of galaxies runs along the axis from one cluster

centre to the other.

2 Warped (Curved). The galaxies lie off the axis and continuously curve

(in a ’C’ or ’S’-shape for example) from one cluster centre to the other.

3 Sheet (Planar; Wall). The filament appears as Type I or II viewed from one

direction but the galaxies are approximately evenly spread out in the

orthogonal view.

4 Uniform. Galaxies fill the space between the clusters in an approximately

uniform manner viewed from any direction.

5 regular (Complex). There are one or more connections between both cluster

centres, but the connections are irregular in shape and often have large density

fluctuations.

to these clusters other clusters fall within the same region of space. These extra

clusters were deemed to be part of the filament if they had a redshift within 0.01 of

the mean redshift of the two initial clusters and were coincident with the filament

galaxies in R.A. and Dec. space. In addition, to confirm the presence of a cluster of

galaxies at the cluster positions, each of the clusters had to have greater than ten

members to be part of the filament. Cluster membership was determined by finding

all 2PIGG (Eke et al., 2004) group centres within 1 h−170 Mpc of the cluster centres.

The members of these groups were then taken as the cluster members. Most clusters

would correspond with a single 2PIGG “group” but for some, the 2PIGG catalogue

had separated the cluster members into multiple “groups”.

From the sample of 432 filaments we created a “clean sample” of filaments. The

filaments had to be between two clear clusters of galaxies and have to be relatively

clean from contamination from other filaments and clusters. Therefore, by a visual

inspection of the 432 filaments, 52 pairs of clusters on these filaments that had a

clear run of galaxies, with no other intruding clusters within 6 h−170 Mpc, were found.


These can be seen in Table 5.2. To avoid contamination from the complex weave

of other filaments, and to enable comparisons with our previous work, the galaxies

joining the two filament clusters were selected using the prolate spheroid method as

described in section 4.2.1. This resulted in 6,222 galaxies within the 52 filaments.

As in Chapter 4 all references to 2dFGRS galaxies are taken from the 2PIGG

subsample of the 2dFGRS (Eke et al., 2004) comprising 191,328 galaxies. This

subsample had all the galaxies within fields with less than 70% completeness, and in

all sectors (overlapping field areas) with completeness less than 50%, removed This

enables comparisons with 2PIGG statistics to be made without bias.

Table 5.2: Filament information for the 52 visually selected sample.

Clusters Mean redshift Filament length

Abell 2829 Abell 0118 0.1133 20.75

Abell 3094 Abell S0333 0.0675 13.07

Abell 1419 Abell 1364 0.1072 27.51

Abell 1411 Abell 1407 0.1334 21.41

Abell 1692 Abell 1663 0.0834 17.41

Abell 1620 Abell 1663 0.0839 21.58

Abell 2553 EDCC 0275 0.1458 13.05

Abell 3980 EDCC 0268 0.1894 27.04

APMCC 0869 APMCC 0840 0.1125 47.62

Abell 2601 Abell 4009 0.1091 42.68

EDCC 0365 Abell S1155 0.0547 38.71

Abell 2741 APMCC 0039 0.1050 12.92

Abell 2780 APMCC 0039 0.1031 33.62

EDCC 0465 Abell 2780 0.1046 40.13

Abell 2741 APMCC 0051 0.1060 21.07

EDCC 0445 APMCC 0094 0.0617 17.94

APMCC 0094 EDCC 0457 0.0613 20.86

continued on next page



EDCC 0465 Abell 2814 0.1084 12.44

Abell 2814 Abell 2829 0.1097 22.08

Abell 2734 EDCC 0445 0.0623 17.94

EDCC 0457 EDCC 0445 0.0620 10.24

Abell 2829 EDCC 0511 0.1112 23.01

EDCC 0517 EDCC 0511 0.1107 19.03

Abell 2878 EDCC 0511 0.1090 24.14

Abell 2915 EDCC 0581 0.0862 23.51

APMCC 0167 Abell S0160 0.0688 7.98

Abell 2943 APMCC 0222 0.1498 21.36

Abell 2961 APMCC 0245 0.1242 25.60

Abell 2967 Abell 2972 0.1122 12.03

Abell 2981 Abell 2999 0.1083 15.84

EDCC 0119 Abell 3837 0.0885 28.84

EDCC 0057 Abell 3837 0.0922 25.07

EDCC 0057 APMCC 0721 0.0963 30.55

Abell 3878 Abell 3892 0.1179 22.31

EDCC 0230 APMCC 0827 0.1103 15.80

APMCC 0827 Abell 3892 0.1142 31.64

EDCC 0128 Abell 3880 0.0586 15.12

Abell 3959 APMCC 0853 0.0876 17.09

Abell S1075 Abell 3978 0.0854 26.87

EDCC 0457 Abell 2794 0.0613 20.86

EDCC 0492 Abell 2804 0.1169 44.83

EDCC 0202 EDCC 0187 0.0768 8.85

EDCC 0187 APMCC 0810 0.0769 7.24

EDCC 0317 Abell 4011 0.1371 8.76

continued on next page

5.4. Star formation properties 103


EDCC 0321 Abell 4012 0.0533 9.49

Abell 3854 Abell 3844 0.1505 29.89

Abell S1064 EDCC 0153 0.0571 17.95

Abell 2967 Abell 2981 0.1103 16.12

EDCC 0239 APMCC 0853 0.0871 17.62

EDCC 0248 Abell 3959 0.0876 17.09

EDCC 0217 EDCC 0202 0.0784 19.94

Abell 2493 EDCC 0215 0.0773 21.88

Abell 2493 EDCC 0215 0.0773 21.88

5.4 Star formation properties

5.4.1 Properties of galaxies in the field

It has been shown on many occasions (Dressler, 1980; Couch & Sharples, 1987;

Balogh et al., 1998) that star formation is suppressed in cluster cores and then

increases with decreasing galaxy density away from the dense cores. Here we seek to

confirm this for the 2dFGRS using the star formation parameter η which is described

in detail in Section 2.5.

The distance of each of the 191,328 2dFGRS galaxies was calculated from the

nearest 2PIGG group of ≥ 30 members (the equivalent of a rich cluster). This was

done for all 2dFGRS galaxies with a measured η value which comprised 167,602

galaxies. The galaxies were then binned in distance in 0.5 h−170 Mpc bins within

the approximate cluster bounds of 2.5 h−170 Mpc. Around the 3 h−1

70 Mpc region of

interest, from past results, 0.1 h−170 Mpc bins were used, while beyond this 1 h−1

70 Mpc

bins were used. These small bin sizes were only possible due to the large sample

size.

It can be seen in Fig. 5.1 that our results agree with the literature, with the

star formation being at a minimum within the cluster cores and gradually rising

with increasing distance from the core and hence decreasing galaxy density. The

means of this sample are taken as a field level with which other distributions can be


Figure 5.1: (a, Top) For galaxies with a measured η, from the entire 2dFGRS (N=167602),

the mean η as function of distance from the nearest cluster (defined as 2PIGG groups with ≥ 30

members) is shown. Finer bins are chosen between 2–4 h−1

70Mpc to investigate the presence of

enhanced SFR in this region. (b, Bottom) For the same galaxies as in a the fraction of these

galaxies with an η < −1.4 is shown as a function of distance from the nearest cluster. (§5.4.1)

compared.

5.4.2 Star formation in galaxies belonging to filaments

Once the members of each filament had been determined the same method used

in their selection was used to find the distance of each filament member from the

nearest of the two clusters at either end. The distances were then binned with the

first two bins extending out to 2.14 h−170 Mpc (Abell radius) to contain all the cluster

galaxies. The area of greatest interest just outside of the cluster was covered in

0.25 h−170 Mpc bins while in the outer regions 2 h−1

70 Mpc bins were used. Within

each bin the mean η was calculated. The data for galaxies from all the filaments

were combined and the means plotted against the mean distance in each bin and

can be seen in see Fig. 5.2. For comparison between the trend with distance for

the filament galaxies with galaxies elsewhere, we take the field values calculated in

section 5.4.1, shown as the dashed line. We also plot, in the bottom panel, the

fraction of passive (η<−1.4) galaxies in each bin.


Figure 5.2: (a, Top)For the “clean filament” sample (N=52), the mean η of each galaxy as

function of distance from the nearest cluster is shown. The dashed line shows the mean η as

function of distance from the nearest cluster (defined as a 2PIGG group with ≥ 30 members) for

all 2dFGRS galaxies. (b, Bottom) For the same galaxies as in the top panel the fraction of these

galaxies with an η < −1.4 is shown as a function of distance from the nearest cluster. The dashed

line showing the same fraction as a function of distance from the nearest 2PIGG group with ≥ 30

members for the whole 2dFGRS. (§5.4.2)

Fig. 5.2 shows, as expected, the mean η and hence SFR is at a minimum in the

first bin, within the cluster and the fraction of passive galaxies is at a maximum.

The field value shown as a dotted line on average has a gradual increase in SFR with

increasing distance from the cluster centre. However, the filament galaxies show a

distinct peak in the gradual increase in SFR at approximately 2.5 h−170 Mpc. This

region corresponds to about 1.5 virial radii. This is in agreement with the results of

the Pisces-Cetus filaments used in Chapter 4. There is a very slight corresponding

dip in the percentage of passive galaxies in the 2.0–2.5 h−170 Mpc range.

Fig. 5.3 shows a histogram of the values of η for each of the 8 bins for the

galaxies of the 52 filaments and the field. It can be seen that the mean η value for

the field represented by the dashed vertical line increases gradually with increasing

bin number while the filament galaxies have a peak in bin 4. It can be seen in the

histograms, that in bin 4, there is a reduction in the number of filament galaxies

in the first passive peak and a slight increase in the numbers above this at higher


Figure 5.3: For the “clean filament” sample (N=52), histograms of the η parameter for the

galaxies in each of the 8 distance bins are shown in red. The corresponding histograms for the field

galaxies are shown in green. The mean η in each bin is shown as a dashed vertical line. (§5.4.2)


Figure 5.4: (a, Top)For the “clean filament” sample (N=52), the mean η as function of distance

from the nearest cluster is shown. Giant galaxies (M < −20) are shown as closed circles while

dwarf galaxies (M > −20) are shown as open triangles. (b, Bottom) For the same galaxies as in a

the fraction of these galaxies with an η < −1.4 is shown as a function of distance from the nearest

cluster. (§5.4.3)

values of η for the filament galaxies with respect to the field.

5.4.3 Star formation in giant and dwarf galaxies

Continuing the investigation of star formation with respects to environment, the

“clean filament” sample (N=6,222 galaxies) was further segregated by environment

into giant and dwarf galaxies. The samples were defined as giant galaxies (MB ≤−20) and dwarf galaxies (−20 < MB ≤−17.5) of 1,392 galaxies and 4,830 galaxies

respectively.

As before we plot the mean value of η, and the fraction of passive galaxies, as

a function of their distance from the nearest cluster, which can be seen in Fig. 5.4.

However, the two separate samples are now plotted as open triangles for dwarf

galaxies and filled circles for giant galaxies.

It seems that the peak in mean η seen in Fig. 5.4, at approximately 2.5 h−170 Mpc,

is almost entirely due to enhanced star formation in dwarfs. This is in agreement

with our results for the Pisces-Cetus filaments. The two populations are completely


segregated with the dwarf galaxies having more SFR at all distances. This is in good

agreement with Haines et al. (2006a) who gets a lower fraction of passive galaxies

in giants for all values of local density.

As in Chapter 4 it is worth remembering that the populations were determined

from the blue magnitudes. The blue magnitude will be boosted by star formation

and therefore the high η galaxies will have preferentially higher blue magnitudes.

However, this effect would serve to pull the two populations closer together so the

real separation may be even greater than that seen here.

5.4.4 Star formation in short and long filaments

Continuing the investigation of star formation with respects to environment, the

“clean filament” sample (N=6,222 galaxies) was further segregated by environment

into those falling in short filaments (length ≤ 15 h−170 Mpc) and long filaments

(length > 15 h−170 Mpc). The samples had of 1,452 galaxies and 4,770 galaxies

respectively.

As before we plot the mean value of η, and the fraction of passive galaxies, as

a function of their distance from the nearest cluster, which can be seen in Fig. 5.5.

However, the two separate sample are now plotted as open triangles for long filament

galaxies and filled circles for short filament galaxies.

The peak in mean η seen in Fig. 5.5, at approximately 2.5 h−170 Mpc, is seen

in both samples. However, there is some evidence that the short filament galaxy

sample peak is higher than that of the longer filament sample. In fact in general the

shorter filament sample galaxies have a higher SFR. This is reflected in the fraction

of passive galaxies which is in general lower for the shorter filaments.

5.4.5 Star formation in groups

The suppression of star formation with increasing local density of galaxies has been

observed to occur at very low values of the local projected density (∼1 h−170 Mpc−2

(e.g. Lewis et al., 2002; Gomez et al., 2003), indicating that the cause does not lie

entirely in the influence of the cluster environment. One suggestion is that much of


Figure 5.5: (a, Top)For the “clean filament” sample (N=52), the mean η as function of distance

from the nearest cluster is shown. Short filament (length≤ 15 h−1

70Mpc) galaxies are shown as

closed circles while long filament (length > 15 h−1

70Mpc) galaxies are shown as open triangles. (b,

Bottom) For the same galaxies as in a the fraction of these galaxies with an η < −1.4 is shown as

a function of distance from the nearest cluster. (§5.4.4)

the evolution of galaxies occurs in groups during their life on the filaments, before

the groups are assimilated in clusters. If so, the trend seen in the previous section

would be different for filament galaxies that belong to groups and those that are

relatively isolated.

As in Chapter 4 We therefore split our galaxy sample into those that are a

member of a group and those that are not. A group member is defined to be a

member of a 2PIGG group (Eke et al., 2004) that has 4 or more members and a

non-group or relatively isolated galaxy is defined as a galaxy which is not a member

of a 2PIGG group of any number of members. The majority of the galaxies are part

of groups with 4,921 falling in this category, with 669 galaxies being classified as

relatively isolated. As in the other sections the mean value of η, and the fraction of

passive galaxies, as a function of their distance from the nearest cluster are plotted

in Fig. 5.6.

Fig. 5.6 shows the variation of mean η and the fraction of passive galaxies for

these two subsamples, as a function of the distance from the nearest cluster for the

filament galaxies. The mean η is seen to occur in groups and non-group galaxies at


approximately the same distance, but with the non-group galaxies generally having

a higher fraction of star forming galaxies.


N ≥4) in the 52 filaments to similar group galaxies elsewhere in the 2dFGRS. The

black dots represent the variation of mean η and passive galaxy fraction as a function

of distance from the nearest cluster in the 2dFGRS (defined as 2PIGG groups with

N ≥30).

In agreement with the results of Chapter 4 the plots suggest that the star forma-

tion rate is more or less uniform in all groups galaxies irrespective of their distance

from the nearest cluster, except for those galaxies within the virial radii of clusters.

There is some indication that the trend we find of a peak in SFR at approximately

2.5 h−170 Mpc is seen in the group galaxies that belong to filaments, indicating that

the presence of the filaments influences star formation properties in galaxies that

belong to groups in this region. In general the non-group galaxies are seen to have

higher mean values of η and a lower fraction of passive galaxies than the group

galaxies both in the filament and in the 2dFGRS as a whole.

In the same manner as in Chapter 4 we have investigated whether the groups that

we were comparing the SFR in were the same basic entities in the filaments and in the

whole 2dFGRS. We have therefore plotted histograms of the richness and velocity

dispersion for these group samples. These histograms can be seen in Fig 5.8a and

Fig 5.8b. It can be seen, that in agreement with the smaller group sample in Chapter

4, the filament groups (green histograms) have a higher proportion of richer galaxies

and higher proportion with larger velocity dispersions. This is not unexpected as

the filamentary nature of the region will cause the percolation algorithm that the

groups were formed by to pick out more group members and hence the groups have

larger velocity dispersions.

5.4.6 Welch’s test results

As in Chapter 4 we have used Welch’s t test to determine if the means of our two

populations are distinct from one another. Applying Welch’s t test to the mean η

in each bin of our SFR as a function of distance from the centre of a cluster gives


Figure 5.6: (a, Top)For the “clean filament” sample (N=52), the mean η as a function of

distance from the nearest cluster. Galaxies that are members of groups and part of the filament

are shown as crosses while galaxies that are not part of a group are shown as squares. A group is

defined as a 2PIGG group with greater than or equal to 4 members, while non-group galaxies are

those 2PIGG groups which are not part of a group of any number of members. The dashed line

shows the mean η for non-group galaxies in the whole 2dFGRS, while the dot-dashed line shows

the mean η for group galaxies in the whole 2dFGRS. (b, Bottom) The fraction of filament galaxies

with η < −1.4 as a function of distance from nearest cluster within the same galaxy and group

samples as defined for a. (§5.4.5)

the results seen in Table 5.3. The joint probability for the filament region outside

of the cluster radius (bins 4-9) is also shown in Table 5.3.

It can be seen that for Fig. 5.2 the point at which the SFR of the filament

galaxies peaks has a probability of 0.03 of the means being equal. This corresponds

approximately 2.0 σ result, which while still not overwhelmingly significant, it is

an improvement on the 1.5 σ result of Chapter 4, strengthening the reality of the

enhancement. Furthermore, reproducing the results of our earlier work of just one

and three filaments, in various samples within 52 filaments, enhances the robust-

ness of our results beyond that shown by the formal significance. The lowest joint

probability is again for the giant and dwarf populations of Fig. 5.4, although most

of the joint probabilities are so small as to make them effectively zero.

5.5. Star formation in the PIM04 sample filaments 112

Figure 5.7: (a, Top)For the “clean filament” sample (N=52), the mean η as a function of

distance from the nearest cluster. Galaxies that are members of groups and part of the filament

sample are shown as crosses This is compared to galaxies that are part of groups within the entire

2dFGRS shown as a dashed line. A group is a 2PIGG group with greater than or equal to 4

members, while non-group galaxies are those 2PIGG groups which are not part of a group of any

number of members. (b, Bottom) The fraction of filament galaxies with η < −1.4 as a function of

distance from nearest cluster within the same galaxy and group samples as defined for a. (§5.4.5)

5.5 Star formation in the PIM04 sample filaments

We have shown that within filaments of galaxies which meet our tight definition for

a “clean filament” there is a marked difference between filament galaxies and the

rest of the field. In this section we investigate whether the same trends are seen

within the more broadly defined filaments of the PIM04 sample.

We take two filament samples from the PIM04 sample, the length of filament

being between 10 and 40 h−170 Mpc in each. From these filaments we extract the

Table 5.3: Welch’s test results for “clean sample” filamentsFigure Probability

number 1 2 3 4 5 6 7 8 9 Joint (4-9)

Fig. 5.2 0.02 0.87 0.97 0.08 0.03 0.04 0.06 3.9E-3 6.5E-3 1.8E-9

Fig. 5.4 1.1E-6 6.23E-10 0.24 0.001 0.04 3.9E-13 2.5E-10 1.5E-9 0.02 1.2E-36

Fig. 5.5 0.23 0.03 0.65 0.59 0.88 0.06 0.05 0.65 0.56 5.7E-4

Fig. 5.6 0.86 0.37 0.98 3.7E-5 0.003 4.3E-7 4.2E-5 4.5E-19

Fig. 5.7 0 0.09 0.53 0.47 0.76 3.2E-5 0.003 2.9E-5 3.0E-5 2.9E-17


Figure 5.8: (a, Left)Histograms of the relative number of groups with richness 0-25 for groups

(2PIGG groups with N ≥ 4) within the 52 filaments of the clean filament sample (green) and

groups within the entire 2dFGRS (Red). (b, Right) Histograms of the relative number of groups

with velocity dispersion 0-1000 kms−1 for groups within the 52 filaments of the clean sample (green)

and groups within the entire 2dFGRS (Red). (§5.4.5)

galaxies that formed the orthoginal plains used in the classification process and

remove any repeated galaxies. The samples were defined as:

1. Galaxies from filaments classified as type 1, straight or 2, warped in the PIM04

sample. This resulted in 307 filaments and 24,420 galaxies (PIM04a).

2. Galaxies in filaments of all types including those that are classified as being

near coincidental clusters and as not being a filament. This resulted in 552

filaments and 35,609 galaxies (PIM04b).

5.5.1 Star formation within the filaments

As in the other sections the mean value of η, and the fraction of passive galaxies,

as a function of their distance from the nearest cluster are plotted for each of the

samples.

The galaxies of PIM04a while being from more broadly defined definition of

filament than ours, the filament type is still constrained. It can be seen in Fig. 5.9

that while the peak in mean η at approximately 2.5 h−170 Mpc is less pronounced than

that in our own filaments there is definite evidence for a peak in mean η and a very

slight dip in the fraction of passive galaxies.. However, one difference to note is that


for this sample the majority of the points fall under the field value, with only the

peak values approaching field levels. This can also be seen in Fig. 5.11 where the

mean in each bin of the PIM04a sample shown in red is below that of the field. It

can be seen that in most bins the red histogram is above the green for the lower η

values below -2.0. This is in contrast to the results of our tightly defined filaments

where only the higher radii points drop significantly below the field, and the results

of Chapter 4 where the filament points closely follow the field and the peak values

are well above it.

The galaxies of PIM04b include all of the potential filaments and thus will include

those that are complex, coincidental clusters and even those classified as not being

a filament. Therefore, these galaxies will simply be from the regions between two

clusters with the potential to be a filament. The resulting plot can be seen in

Fig. 5.10 and there is little or no evidence for a peak at 2.5 h−170 Mpc in this very

loose definition of filament. Once again the points are below that of the field values

with not even the peak reaching the field level.

5.5.2 Star formation within giants and dwarfs

For the PIM04a galaxies which have shown some evidence for the trends seen in

our other work the 24420 galaxy sample was further segregated by environment into

giant and dwarf galaxies. The samples were defined as giant galaxies (MB ≤−20) and

dwarf galaxies (−20<MB ≤−17.5) of 5867 galaxies and 18553 galaxies respectively.

As before we plot the mean value of η, and the fraction of passive galaxies, as a

function of their distance from the nearest cluster, which can be seen in Fig. 5.12.

However, the two separate sample are now plotted as open triangles for dwarf galax-

ies filled circles for giant galaxies.

Fig. 5.12 again shows the results to be consistent with our previous results both

in this Chapter and Chapter 4 and with the results of Haines et al. (2006a), with

the dwarf galaxies having a higher mean SFR at all distances. The peak at ap-

proximately 2.5 h−170 Mpc is clearly seen in the dwarf galaxies once again with slight

evidence for a corresponding dip in the fraction of passive galaxies. The same peak

is a little more ambiguous in the giant galaxies with only the two outside points of


Figure 5.9: (a, Top)For galaxies within the filaments of PIM04a of the PIM04 sample , the mean

η as function of distance from the nearest cluster is shown. The dashed line shows the mean η as

function of distance from the nearest 2PIGG group with ≥ 30 members for all 2dFGRS galaxies.

(b, Bottom) For the same galaxies as in a the fraction of these galaxies with an η < −1.4 is shown

as a function of distance from the nearest cluster. The dashed line showing the same fraction as

a function of distance from the nearest 2PIGG group with ≥ 30 members for the whole 2dFGRS.

(§5.5.1)

the four normally associated with the peak actually being at a raised value.

5.5.3 Star formation in groups

As before we split our PIM04a filament galaxies into those that are a member of

a group and those that are not. A group member is defined to be a member of a

2PIGG group (Eke et al., 2004) that has 4 or more members and a non-group or

relatively isolated galaxy is defined as a galaxy which is not a member of a 2PIGG

group of any number of members. A larger percentage of the galaxies are part of

groups with 11,204 falling in this category, with 7,457 galaxies being classified as

relatively isolated. As in the other sections the mean value of η, and the fraction of

passive galaxies, as a function of their distance from the nearest cluster are plotted

in Fig. 5.13.

Fig. 5.13 shows the variation of mean η and the fraction of passive galaxies for

these two subsamples, as a function of the distance from the nearest cluster for


Figure 5.10: (a, Top)For galaxies within the filaments of PIM04b taken from the PIM04 sample

, the mean η as function of distance from the nearest cluster is shown. The dashed line shows the

mean η as function of distance from the nearest 2PIGG group with ≥ 30 members for all 2dFGRS

galaxies. (b, Bottom) For the same galaxies as in a the fraction of these galaxies with an η < −1.4

is shown as a function of distance from the nearest cluster. The dashed line showing the same

fraction as a function of distance from the nearest 2PIGG group with ≥ 30 members for the whole

2dFGRS. (§5.5.1)

the filament galaxies. It can be seen in Fig. 5.13 that the peak in mean η seen

at approximately 2.5 h−170 Mpc for all the PIM04a filament galaxies in section 5.5.1

is mainly due to the group galaxies, with the non group galaxies actually having

a dip in mean η in the same region. This is matched by a corresponding peak in

the fraction of passive galaxies for the non-group galaxies and a dip in the group

galaxies. However, the large errors on the non group galaxies leaves the possibility of

a sizable contribution from these galaxies to the peak in mean η for this sample and

an equal possibility of little contribution from the non group galaxies of our previous

results. In agreement with all of our previous results the non group galaxies are in

general at higher mean values of η and lower fractions of passive galaxies.


N ≥ 4) within PIM04a and group galaxies elsewhere in the 2dFGRS. The dashed

line represent the variation of mean η and passive galaxy fraction as a function of

distance from the nearest cluster in the 2dFGRS. In agreement with our previous


Figure 5.11: For galaxies within the filaments of PIM04a taken from the PIM04 sample , a

histogram of η within each of the 15 distance bins is shown in red. The equivalent histogram but

for the field sample is shown in green. The mean eta in each bin is shown as a dashed vertical line.

(§5.5.1)

5.6. Conclusions 118

Figure 5.12: (a, Top)For the PIM04a galaxies, the mean η as function of distance from the

nearest cluster is shown. Giant galaxies (M < −20) are shown as closed circles while dwarf galaxies

(M > −20) are shown as open triangles. (b, Bottom) For the same galaxies as in a the fraction

of these galaxies with an η < −1.5 is shown as a function of distance from the nearest cluster.

(§5.5.2)

results there seems to be little evidence of a peak in the mean η of group galaxies in

the whole 2dFGRS beyond the fluctuations introduced through the increase in bins

from the earlier work. There is though some evidence for a peak in the filament

group galaxies mean η at approximately 2.5 h−170 Mpc. In the same manner as the

results for all the filament galaxies in section 5.5.1 the filament group galaxies are

in general at lower mean values of η and higher fractions of passive galaxies than

the groups in the 2dFGRS as a whole.

5.6 Conclusions

We have investigated the environmental dependence of star formation within fila-

ments of galaxies with quite stringent criteria. These filaments have to be between

just two clusters of galaxies and the filaments have to have no intervening clusters

within 6h−170 Mpc. Within this “clean sample”, star formation variation has been

observed by finding the variation of the η parameter with distance from the cluster

centres along the filaments.


Figure 5.13: (a, Top)For the galaxies of PIM04a, the mean η as a function of distance from

nearest cluster. Galaxies that are members of groups and part of the filament are shown as crosses

while galaxies that are not part of a group are shown as squares. A group is a 2PIGG group with

greater than or equal to 4 members, while non-group galaxies are those 2PIGG groups which are

not part of a group of any number of members. (b, Bottom) The fraction of filament galaxies with

η < −1.4 as a function of distance from nearest cluster within the same galaxy and group samples

as defined for a. (§5.5.3)


Figure 5.14: (a, Top)For the galaxies of PIM04a, the mean η as a function of distance from

nearest cluster. Galaxies that are members of groups and part of the filament are shown as crosses

This is compared to galaxies that are part of a group within the entire 2dFGRS shown as a dashed

line. A group is a 2PIGG group with greater than or equal to 4 members, while non-group galaxies

are those 2PIGG groups which are not part of a group of any number of members. (b, Bottom)

The fraction of filament galaxies with η < −1.4 as a function of distance from nearest cluster

within the same galaxy and group samples as defined for a. (§5.5.3)

For galaxies belonging to the “clean sample” filaments we have looked at the

variation of the mean η parameter with distance along the filaments, in bins ranging

from 0.25 h−170 Mpc within the 2-3 h−1

70 Mpc region up to 2 h−170 Mpc, starting from

the cores of the rich clusters out to the sparser reaches of the filament. We have

also looked at similar dependence on distance of the fraction of passive galaxies,

in each distance bin. In doing so, we have also noted whether these galaxies are

giant (MB ≤−20) or a dwarf, member of a group or a cluster, or are part of a short

filament (length≤ 15 h−170 Mpc) or long. Where possible, we have compared these

results to similar properties of galaxies elsewhere in the 2dFGRS galaxy redshift

survey.

We confirm that in the cores of rich clusters, the star formation rate in a galaxy

is very low, irrespective of its mass, by showing that the value of mean η and the

fraction of passive galaxies falls to its lowest value for both giant and dwarf galaxies

in the cores of clusters. As one moves away from the cores of clusters along the


filaments, there is an increased activity of star formation, peaking at approximately

2.5 h−170 Mpc, at approximately 1.5 times the virial radius of the clusters. This peak

in star formation in filament galaxies is seen to be mostly due to dwarf galaxies

(−20 < MB ≤−17.5). All of this is in agreement with the much smaller sample of

filament galaxies used in Chapter 4. More luminous galaxies (MB ≤−20) have much

lower star formation than less luminous galaxies at all distances from the centre of

the cluster. This is in better agreement with the results of Haines et al. (2006a)

than for the smaller sample in Chapter 4 where there was some overlap at lower

radii. The peak in SFR is observed in both the short and long filaments at the same

distance, but with the short filaments having higher SFR in the peak and higher

SFR in general.

With the increased numbers in the “clean sample” compared with the Pisces-

Cetus sample of Chapter 4, it is more clear that in filaments the mean η of the

non-group galaxies are at much higher values than the group galaxies. However,

this does not appear to be an effect of the filament, with the non-group galaxies

within the whole 2dFGRS showing a similar enhancement in mean η over the group

galaxies.

It is also seen that there is little variation in mean η with distance for the group

galaxies taken from the whole 2dFGRS. This is in contrast with the group galaxies

within the filaments which again show a peak at approximately 3 h−170 Mpc. This

would suggest that the effects such as galaxy harassment are more important in the

denser filament environment and effects all galaxies, including those in groups.

We have also investigated the same environments and effects in the more broadly

defined filaments of the Pimbblet, Drinkwater, & Hawkrigg (2004) catalogue. While

the peaks in the mean η are less well defined they are clearly present in those

filaments that are designated as being genuine filaments of type 1 or 2, straight

or curved. However, when more dubiously defined filaments are included the peak

becomes less significant. Within the genuine filaments the same general trends in

giant and dwarf, group and non-group distributions are observed as in the “clean

sample” of filaments .

The results of this Chapter closely follow those seen in Chapter 4 and hence the


same physical processes are likely to be the cause of the enhancements in SFR (see

§4.3) seen in this large sample of filaments. Therefore, galaxy harassment will once

again be the most likely candidate for the enhancement in SFR.

Although these results in this work again show interesting environmental ef-

fects on star formation in galaxies and are in agreement with our results for the

Pisces-Cetus supercluster, we have used an indirect measure for star formation (the

η parameter) in these galaxies. It would therefore be prudent to continue the inves-

tigation with a more robust measurement of star formation such as the equivalent

width of the Hα emission line from filament galaxies.

Chapter 6

C.S.Lewis: “You can never get a cup of tea large enough or a book big enough to

suit me”

Star formation in the Shapley

supercluster

6.1 Introduction

Shapley (1930) observed the entire southern sky down to 18th magnitude with the 24

inch Bruce telescope at Bloemfontein, South Africa. He catalogued 76,000 galaxies

and over 40 distinct clusters of galaxies. The most “noteworthy” of these was a

cloud of galaxies in Centaurus. While he could not reliably estimate the population,

he thought that a preliminary account was interesting due to “the great linear

dimensions, the numerous population and the distinctly elongated form”. This cloud

is now known to be the core of the Shapley supercluster in the region around A3556,

A3558 and A3562. He surmised that the cloud in Centaurus contained over 200

galaxies and “obviously was a super system that is important in our considerations

of our own galactic system”. Because of his amazing incites over 50 years before

any real attention was payed to this area, the region was named after him and the

Shapley supercluster was born.

The Shapley supercluster (SSC) is one of the most massive concentrations of

galaxies in the local universe (Raychaudhury, 1989; Scaramella et al., 1989). Con-

sisting of 29 Abell clusters (see §3.1.3) it forms the second largest supercluster in the

catalogue of Raychaudhury et al. (2007). The SSC is centred around R.A.=13h25m

123

6.1. Introduction 124

and Dec.= −30 and has a mean redshift of z = 0.0476. The SSC is approxi-

mately 15 degrees long, corresponding to about 50 h−170 Mpc. The crossing time for

a cluster in this structure would be comparable to the age of the universe. Thus

the SSC can not be thought of as a virialised structure, however it may be over-

dense enough to exhibit different environmental effects to less dense regions. X-ray

work by Raychaudhury et al. (1991) showed the SSC to have a total mass exceeding

1.0 × 1016 h−170 M⊙ and our own work shows it to be 1.2 × 1016 h−1

70 M⊙ (see §3.4.3).

These values imply that the supercluster may be close to turning around and be-

ginning to collapse. However, the values are small enough that the system is likely

to still be in or have only recently left the linear regime. More recently the SSC has

proved to be important in studies of the bulk flow observed in the local universe

(Radburn-Smith et al., 2006).

The SSC is located approximately 140 h−170 Mpc behind the Hydra-Centaurus

Supercluster, which is itself approximately 60 h−170 Mpc from us. The SSC lies in the

general direction of the motion of the local group with respects to the cosmic mi-

crowave background, as inferred from the dipole anisotropy of the cosmic microwave

background (Smoot et al., 1992), and as such is a major contributor to the peculiar

velocity of the local group. Bardelli et al. (2000) found a mean overdensity of over

∼ 11.3 for the central region on a 10 h−1100 Mpc scale. This central region alone was

shown to contribute about 26 km s−1 or 7% to the 366 ± 125 km s−1 (Hoffman,

2001) total tidal velocity of the local group.

In the previous Chapters we have investigated the rate of star formation within

the supercluster and galaxy filament environments. This has been performed with

the use of the 2dFGRS η parameter, which while being shown to have a good relation

to the Hα equivalent width (EW), is still an indirect measure of the star formation.

In this Chapter we will investigate the star formation rates in galaxies within the

SSC environment using the EWs of galaxy emission lines taken from the 6dF survey.

The six Degree Galaxy Survey (6dFGS)

The 6dF galaxy survey has obtained over 120,000 redshifts in the southern sky since

it began in 2001. By the time of its final release in late 2006, the survey will have

6.2. Spectroscopic data 125

covered an area 8 times larger than that of the 2dFGRS (but not to the same depth

in redshift) and obtained peculiar velocities for over 15,000 galaxies. The survey

is performed on the six-degree field multi-object fibre spectroscopy system on the

UKST (6dF).

The 6dF is capable of taking 150 simultaneous spectra over a field of 5.7 degree

diameter. The primary sample for the survey is the near infrared (NIR) two micron

all sky survey (2MASS)(Jarrett et al., 2000). The use of a NIR survey means that

the bias towards currently star forming galaxies, found in the SDSS and 2dFGRS,

would be minimalised. The 2MASS total magnitudes were used where available and

at lower magnitudes an estimate of the total magnitude was taken from isophotal

magnitudes. These magnitudes were used to apply a cut in the K band of less than

12.75, resulting in 113,988 galaxies from the primary sample.

Thirteen other surveys were combined with the primary sample resulting in

174442 galaxies in the final sample, 150000 of which are hoped to be covered by the

survey end. These additional galaxies extend the survey down to (H, J, rf , bJ)=(13.05,

13.75, 15.6, 16.75). The instrument uses a 1032 × 1056 pixel CCD with R and V

reflection gratings covering the wavelength ranges 4000−5600 A and 5500−7500 A

respectively. Examples of combined V and R spectra can be seen in figs. 6.1 to 6.3.

The survey has a median depth of z = 0.05, reaching to approximately z ∼ 0.15.

6.2 Spectroscopic data

Our data consisted of 34,649 galaxies from the entire 6dF survey with redshift of

at least a quality of 3 (probable redshift or better (see Jones et al., 2004)), kindly

supplied by Philip Lah. For this study, we used only star formation measures based

on emission lines. When available the following equivalent emission line widths were

obtained, Hα, Hβ, [OIII](5007 A), [OIII](4959 A), [NII](6584 A) and [NII](6548

A). Of the 34,649 galaxies, 17,015 had a Hα emission line detected. Due to the

difficulty of defining an index with the [NII] lines surrounding the Hα line, Hα and

[NII] emission were measured using the deblending option of the ’splot command’

of the IRAF package. This enabled Gaussians to be fitted to a series of spectral


Figure 6.1: An example of the 6dF spectrum (V and R combined) of the galaxy 139654, which

is part of our Shapley supercluster sample and has been classified as a starburst galaxy in §6.2.

This is characterised by the large Hα emission line at 6875 A, 6563 A in the rest frame. (§6.1)

Figure 6.2: An example of the 6dF spectrum (V and R combined) of the galaxy 60930, which is

part of our Shapley supercluster sample and has been classified as a passive galaxy in §6.2. It can

be seen that there is no Hα emission line at 6869 A, 6563 A in the rest frame. (§6.1)


Figure 6.3: An example of the 6dF spectrum (V and R combined) of the galaxy 736, which is

part of our Shapley supercluster sample and has been classified as an AGN galaxy in §6.2. This is

characterised by the strong [NII] emission line at 6889 A, 6584 A in the rest frame and the strong

[OIII] emission line at 5007 A, 5239 A in the rest frame. (§6.1)

lines and to measure the value of the equivalent width (EW) of each. In order that

’splot’ could consistently find the continuum level to fit Gaussians to the lines, it

was necessary to set the level of the spectrum away from these spectral lines to a

value of exactly one. Even if there was no spectral line present “splot” tries to fit a

Gaussian. This leads to fits being made of noise spikes or the continuum. Therefore,

if a line had its centre more than 7 A from its expected position it was discarded as a

false reading. In addition, if the fitted Gaussian FWHM was below the instrumental

resolution of the 6dF instrument (FWHM=5 A) or very large such that they were

judged to be fits to the continuum rather than real features (FWHM > 12 A), the

measurement was discarded.

6.2.1 Removal of AGN

Baldwin, Phillips, & Terlevich (1981)(BPT) first showed that it was possible to

distinguish type 2 Active Galactic Nuclei (AGNs) from normal star forming galaxies

by considering the intensity ratios of two pairs of emission lines. This process was


refined by Veilleux & Osterbrock (1987) and it has become standard practice to

classify objects in this manner. The exact demarcation between star forming galaxies

and AGN derived from theory and observations has considerable uncertainty. We

used the work of Kewley et al. (2001) who used detailed continuous starburst models

to obtain an empirical limit, below which the galaxies are almost always starbursts

as opposed to AGN. This limit is defined as:

log(OIII/Hβ) > 0.61/[log(NII/Hα) − 0.47] + 1.19 (6.1)

This definition has been applied to the Lah sample and the resulting divide in

the galaxies can be seen in Fig. 6.4. This resulted in 5,977 galaxies being selected as

starbursts. In addition 22,634 galaxies had no Hα measured. These were assumed

to be non star forming galaxies. This results in a sample of 28,611 galaxies after the

removal of the AGNs and will be referred to as the LAH06 sample. The [NII] values

are those of the λ=6584 A line and the [OIII] is the λ=5007 A line of the doublets.

Once only those galaxies that fell within the Shapley supercluster region had been

selected, this resulted in a sample of 769 galaxies, 124 of them with a non zero Hα.

This sample will be referred to as the SHAP769 sample.

Type 1 AGNs are characterised by broad Balmer and other permitted lines

along with strong emission in the forbidden lines such as [OIII](λ=5007 A) and

[NII](λ=6584 A). Type 2 AGN have the same narrow forbidden lines but without

the broad permitted lines. The [NII](Λ=6584 A) forbidden line in type 2 AGNs is

stronger with respect to Hα than in HII region objects (normal starbursts). Colli-

sional excitation of this line is more important in objects in regions that are partially

ionised. Narrow line AGNs have a significant fraction of non thermal emission in

the X-ray range. This causes a large region of Hydrogen atoms to become partially

ionised resulting in more [NII](Λ=6584 A) emission than in the HII region objects

where emission is due to UV photons emitted by hot OB stars. The region of par-

tial ionisation also has a higher number of photons that can ionise [OII] resulting in

more [OIII](Λ=5007 A) than in all but the most excited [HII] region objects. Thus

type 2 AGN will have stronger EW [NII](Λ=6584 A) lines with respect to the EW

of the Hα line and strong EW [OIII](Λ=5007 A) lines with respect to the EW of


Figure 6.4: BPT diagram (used to distinguish type 2 AGNs from normal star forming galaxies)

of galaxies within the Shapley supercluster region from 6dFGS spectra. The line shown is from

the relation of Kewley et al. (2001) with red galaxies being categorised as AGN and the blue as

normal star forming galaxies.(§6.2.1)

Hβ and be in the top right section of the BPT diagram.

6.2.2 Stellar absorption

It is well known that the Balmer emission lines can suffer contamination due to

underlying stellar absorption and consequently be underestimated. Ideally the EW

of the Hα line would be corrected using a population synthesis model to accurately

model the observed stellar continuum (e.g., Bruzual & Charlot, 2003). This stellar

continuum would then be subtracted from the spectrum of the galaxy.

However, due to time constraints it was not possible to correct the EWs that we

received in this manner. It has been suggested (e.g., Hopkins et al., 2003; Balogh

et al., 2004) that a common correction applied to all galaxies should be sufficient

when dealing with characteristics of an entire sample rather than individual galaxies.

Hopkins et al. (2003) show that an appropriate stellar absorption correction should


be at most +1.3 A. We have therefore added 1.0 A to our Hα and Hβ EWs.

6.2.3 Flux calculations

The 6dF data don’t have spectrophotometric calibrations, so the exact fluxes in

erg s−1 cm−2 will not be known. But since all the spectra were acquired with the

same settings and exposures, and internally calibrated by setting the continuum flux

to the same value we will assume that the equivalent widths can be converted into

fluxes using a factor common to all galaxies.

Rojas et al. (2005) calculates the flux of SDSS Hα lines from,

F (SDSS) =√

2πσκ × 10−17, (6.2)

where σ and κ are the widths and heights of the Gaussian fit to the line and F is

the resulting flux in ergs−1 cm−2. It can be shown that,∫ ∞

−∞κ expx2

dx =√

π (6.3)

It can also be shown that the area under a Gaussian distribution is given by the

left hand side of Eq. 6.4. Since the equivalent width of the line is equal to the area

under the continuum subtracted line, represented by a Gaussian you get that,∫ ∞

−∞κ expy2/2σ2

dy = EW(Hα), (6.4)

where EW(Hα) is the equivalent width of the Hα emission line. Taking x = y

σ√

2

and hence dy = σ√

2 dx leads to,

κσ√

2

∫ ∞

−∞exp−x2

dx = EW(Hα). (6.5)

From Eq. 6.3 this means that,

√2σκ

√π =

√2πσκ = EW(Hα). (6.6)

Therefore, from Eq. 6.2 it follows that,

F (SDSS) = EW(Hα) × 10−17. (6.7)

Our EW(Hα) have been obtained using 3 arcsecond fibres instead of the 7 arcsecond

fibres for the SDSS EW(Hα). Since the ratio of areas of the SDSS fibres to the

2dFGRS fibres is approximately 5 we adopted Eq. 6.8 for our flux calculations.

F = 5 × 10−17 EW(Hα), (6.8)


6.2.4 Dust attenuation

The amount of dust reddening is estimated from the Balmer decrement Hα/Hβ

where the Hα and Hβ EWs have been corrected for underlying stellar absorption

as described above. We follow the method of Moustakas, Kennicutt, & Tremonti

(2006) for correcting for dust reddening. The colour excess due to dust reddening

can be expressed as,

E(Hβ − Hα) ≡ −2.5 log

[

(Hα/Hβ)int

(Hα/Hβ)obs

]

, (6.9)

where E(Hβ−Hα) is the colour excess between the Hβ and Hα wavelengths, (Hα /

Hβ)int) is the intrinsic Balmer decrement and (Hα/Hβ)obs is the observed decrement.

A value of (Hα/Hβ)int = 2.86 is used in Eq. 6.9 (Storey & Hummer, 1995). The

amount of extinction which is due only to the physics of the dust grains and hence

only dependent on wavelength can be represented by an attenuation curve given by,

k(Hα) ≡ A(Hα)E(B-V), (6.10)

where E(B-V) is the broadband colour excess, k(Hα) is the opacity (absorption +

scattering) at the wavelength of the Hα line (6563 A) and A(Hα) is the attenuation

at λ 6563A. From the attenuation curve the colour excess is obtained as,

E(B-V) ≡ E(Hβ − Hα)

k(Hβ) − k(Hα), (6.11)

where k(Hβ) and k(Hα) are the opacity at 4861 and 6563 A respectively, and is

used to find the broadband colour excess. The Calzetti (2001) value of k(Hβ)-

k(Hα) = 1.63 was used. Finally the Calzetti (2001) relation for the attenuated to

intrinsic Balmer line ratio of

Rαβ = 100.4E(B-V)(k(Hβ)−k(Hα)), (6.12)

was used and the flux for each galaxy multiplied by Rαβ .


6.2.5 Aperture correction

Each of the fibres placed on a galaxy will not always contain the entire galaxy, and as

such will not obtain the entire flux. It is therefore a possibility to apply a correction

for this so as to obtain a star formation rate (SFR) for the entire galaxy, as opposed

to just the central region. However, as SFR is not constant across the diameter of a

galaxy this may result in artificially enhancing the SFR of the galaxy. A correction

of the type,

Fc = F (rg/3.5)2, (6.13)

could be applied where, F is the aperture uncorrected flux, Fc is the aperture cor-

rected flux, 3.5 arcseconds is the radius of the fibre and rg is the radius of the galaxy

in arcseconds. However, considering the many uncertainties with this correction it

was decided that this correction would just introduce more noise and so was not

applied.

6.2.6 SFR calculation

The first step to calculate a SFR was to convert our fluxes into luminosities by,

L = F4πD2, (6.14)

where L is the Hα luminosity, F is the Hα flux and D is the distance to the galaxy

in question. Once the luminosity was obtained the SFR was calculated using the

Kennicutt (1998b) relation,

SFR = 7.9 × 10−42 L

erg s−1M⊙yr−1. (6.15)

It must be noted that due to the assumptions used in § 6.2.3 while calculating

our fluxes this SFR will be an uncalibrated SFR (USFR), proportional to the actual

SFR. However, as we are looking at general trends in SFR, this quantity should be

sufficient.

6.3. Samples of galaxies in various environments 133

6.3 Samples of galaxies in various environments

From the SHAP769 sample described in § 6.2 with dust and stellar absorption cor-

rections applied, 3 sub samples were made:

1. Field: All galaxies (n = 28611) in the LAH06 sample. The large numbers in

comparison with the other subsamples means that non cluster galaxies should

be the dominant influence.

2. Supercluster cluster: LAH06 sample galaxies within the Abell radius of each

cluster centre of the Shapley supercluster and ±3000 km s−1 of the cluster

mean velocity (n = 126).

3. Non supercluster cluster: LAH06 sample galaxies within the Abell radius of

each cluster centre that is not listed in the supercluster catalogue of (Ray-

chaudhury et al., 2007) and ±3000 km s−1 of the cluster mean velocity (n =

799).

Fig. 6.5 shows a histogram of the USFR of galaxies in each of the three samples.

The relative number of galaxies in that bin with respect to the total number of

galaxies in the sample is shown. In addition, we plot the same relative numbers,

but relative to the field sample, to emphasise the higher USFR bins. Although the

differences are small it can be seen that the supercluster cluster sample has a higher

percentage of its galaxies in the very low SFR first bin than the other samples. This

may be due to the clusters being in a more dense environment, suppressing SFRs

more than in clusters outside of superclusters. The field has the lowest proportion

of its galaxies in the lowest USFR bin, this being consistent with it having the least

dense galaxy environment.

Things are a little clearer at the high USFR end of the plot. Here it can be

seen that the cluster galaxies belonging to the supercluster do not have any galaxies

present in them beyond an USFR of 0.4. The non-supercluster cluster galaxies

in slightly less dense environments have some galaxies present in bins up to an

uncalibrated SFR of 0.65. The highest USFR bins have only galaxies which are in

the relatively less dense field environment.


Figure 6.5: (a, top)A histogram of the of the uncalibrated star formation rate of galaxies in

the Shapley supercluster region. The histogram shows the relative number of galaxies in that bin

with respects to the total number of galaxies in the sample. The field, non supercluster cluster

and supercluster cluster samples are represented by the blue dot-dash, green dashed and solid red

lines respectively. (b, bottom) The same relative numbers as in a but now also relative to the field

sample. This emphasises the higher uncalibrated star formation bins. The proportion of galaxies

with no star formation for the field, non supercluster cluster and supercluster cluster samples are,

79%, 82% and 91%, respectively. (§6.3)


Figure 6.6: A histogram of the of the uncalibrated star formation rate of galaxies in the Shapley

supercluster region. The histogram shows the relative number of galaxies in that bin with respects

to the total number of galaxies in the sample. The field, non-supercluster cluster and supercluster

cluster samples are represented by the blue dot-dash, green dashed and solid red lines respectively.

The proportion of galaxies with no star formation for the field, non supercluster cluster and su-

percluster cluster samples are, 79%, 82% and 91%, respectively. The first bin of Fig. 6.5 which

includes mainly non-star forming galaxies has been omitted and the Y-axis scaled accordingly to

display the low USFR bins, which never the less have some star formation. (§6.3)

6.4. SFR as a function of distance from a cluster 136

Figure 6.7: Mean uncalibrated star formation rate as a function of distance from the nearest

cluster for galaxies in the Shapley region. The 6 bins in ascending order contain 38,25,20,22,77

and 103 galaxies. (§6.4)

6.4 SFR as a function of distance from a cluster

For each galaxy in the SHAP769 sample the distance from the nearest Shapley clus-

ter was calculated using the co-moving distance formula of Hogg (1999). Distances

were found using the galaxies individual redshifts unless the galaxy was classified as

being a member of a cluster. Due to the lack of a comprehensive cluster catalogue in

this region it was assumed that galaxies within the Abell radius of a cluster centre

and 3000 km s−1 of the mean cluster redshift were cluster galaxies. Due to the in-

creased peculiar velocities with respect to the filament galaxies the distances within

the clusters were calculated at the mean redshift of the clusters. The galaxies were

then binned as a function of the distance from the nearest cluster in 6 increasing

size bins ranging from 0.5h−170 Mpc in the cluster cores up to 3h−1

70 Mpc bins. The

mean uncalibrated star formation rate as calculated in §6.2.6 in each bin was then

calculated and can be seen in Fig. 6.7.

It can clearly be seen that while in general there is a slight slope in increasing

USFR from the inner bins to the outer the mean USFR in bin 3 is much higher

than in any other bin. While this may suggestive of a real effect increasing the

6.5. Fraction of starburst galaxies 137

USFR at approximately 2h−170 Mpc, the error bars are large. There are 20 galaxies

in bin 3 where the peak occurs. With bins 1,2 and 4 having 38, 25 and 22 galaxies

respectively, and having reasonable errors, the large errors are not due to a small

number of galaxies. However, of the 20 galaxies in bin 3, only 2 are star forming

and it is only these two galaxies that pull the mean USFR up to such a high value,

which results in the large errors seen.

6.5 Fraction of starburst galaxies

Within the Shapley supercluster region there were 176 galaxies which had the 4

appropriate emission indices to be processed by the BPT diagram to remove AGN

as described in §6.2.1. Of these galaxies, 124 were selected as being starburst galaxies

rather than AGN. The distances from the nearest cluster in the Shapley supercluster

were again calculated for each galaxy in these two samples and the fraction of

galaxies in each bin that were starburst galaxies was calculated. The resulting

plot can be seen in Fig. 6.8. There seems to be little variation in the percentage of

starburst galaxies with distance from the nearest cluster, which would agree with

the results of Miller et al. (2003). However, it can be seen that the small number

of galaxies in the sample (n = 15 per bin) results in large error bars on each point

and hence the significance of the results is reduced.

6.6 Fraction of passive galaxies

Out of the 769 galaxies in the SHAP769 sample 645 are classified as being passive

or having no Hα emission line. In this section we have calculated the fraction of

galaxies in each distance bin that are passive. It can be seen in Fig. 6.9 that as

expected the maximum number of passive galaxies are found in the first bin within

the cluster core. From this lowest value the fraction of passive galaxies is seen to

steadily decrease with increasing distance from the cluster centre. No corresponding

dip in the fraction of passive galaxies is seen in the 2h−170 Mpc region. However, once

again the errors are very large on all the points giving a small significance to the


Figure 6.8: Fraction of starburst galaxies as a function of distance from the nearest cluster for

galaxies in the Shapley region. (§6.5)

results.

6.7 Conclusions

For the galaxies lying in the region of the sky covered by the Shapley supercluster,

we have investigated the evidence of enhanced star formation in clusters within

and outside the supercluster. This has been performed using an uncalibrated star

formation rate (USFR) derived from the equivalent width of the Hα emission line

from 6dF spectroscopic data. Galaxies that are found to be AGN have been removed

and corrections applied to the USFR for underlying stellar absorption and dust

reddening.

We found that, as expected, cluster galaxies have evidence of suppressed star

formation compared to galaxies in the field, but also that SFR is more suppressed

within clusters in the more dense supercluster environment.

We have also investigated the environmental dependence of star formation within

the Shapley supercluster. We have done this by finding the variation of the USFR

with distance from the centre of the nearest cluster which is a member of the super-


Figure 6.9: Fraction of passive galaxies as a function of distance from the nearest cluster for

galaxies in the Shapley region. (§6.6)

cluster. It is well known that in the cores of rich clusters, the star formation rate

in a galaxy is very low. We confirm that this is also the case for our supercluster

galaxies, with the lowest mean USFR being found in the lowest distance bin. As one

moves away from the cores of clusters, there is a very gradual increase in the mean

USFR out to 10h−170 Mpc, but with a peak in the mean USFR at approximately

2h−170 Mpc. The gradual decrease in USFR towards the core, as discussed in §4.3,

will most likely be due to galaxies encountering the Intra Cluster Medium (ICM)

and an increasing density of galaxies. The galaxies will start to lose their warm gas

haloes through ram pressure stripping and evaporation as the galaxys’ gas interacts

with the hot ICM.

We also take a look at the fraction of galaxies that are starbursts as opposed to

AGN as a function of distance from the cluster cores. These results seem to show

little evidence for any variation in AGN percentage with distance. However, larger

numbers of galaxies would be needed to conclusively prove this.

Finally we look at the fraction of passive galaxies as a function of distance from

the cluster centres. As expected the fraction was at a maximum within the cores and

gradually decreased with increasing distance from the core. However, once again a


large sample of galaxies would be needed to conclusively prove this.

The results for this Chapter have once again been indicative of interesting en-

vironmental effects on star formation in galaxies. In comparison with the work in

previous Chapters using the η parameter the USFR with its corrections for dust

and the underlying star population is a better representation of the SFR trends

within the environment. However, the overall results have suffered from small num-

ber statistics and a larger sample of galaxies is needed to conclusively prove the

observed trends.

Chapter 7

Margaret Thatcher: “If my critics saw me walking over the Thames they would say

it was because I couldn’t swim.”

Conclusions

7.1 Summary of main results

We have used survey redshifts (2dFGRS, 6dFGS, SDSS, NED and ZCAT) of galaxies

to investigate the nature, extent and orientation of the Pisces-Cetus, Shapley and

Horologium-Reticulum superclusters. This has been combined with photometric

data from SuperCosmos to obtain estimates of the virial mass of clusters belonging

to the superclusters and hence obtain minimum masses for the superclusters. These

have shown the superclusters to only have mass overdensities of a few times the

critical density of the universe over scales of several tens of h−170 Mpc and to still be

in or have only recently left the linear regime. Thus they are good candidates for

studying the processes present in their formation. Furthermore, this confirms that

structures of the order of a 100 h−170 Mpc are structures in their own right and hence

may have different environmental effects on the evolution of galaxies.

We have used the 2dFGRS star formation rate (SFR) parameter η, which is

related to the equivalent width of the Hα emission line, to show that the SFR

properties of galaxies within the filaments of the Pisces-Cetus supercluster show

interesting environmental effects. The SFR shows a gradual decrease from the pe-

riphery of the filament into the cluster core consistent with galaxies losing their

warm gas haloes through ram pressure stripping and evaporation as the gas belong-

ing to the galaxy interacts with the hot Intracluster Medium. However, on top of

this monotonic trend with decreasing distance from the centre of a cluster, we find

141

7.1. Summary of main results 142

a nearly instantaneous enhancement of the SFR at ∼ 3 h−170 Mpc from its centre,

which is about 1.5–2 times the virial radius of the cluster.

We conclude that the most likely reason for this sudden enhancement in SFR is

either the first encounter of the infalling galaxies with the hot intracluster medium

of the cluster, or galaxy-galaxy harassment due to the rapid increase of the space

density of galaxies infalling along the filaments at these distances. The abruptness

of the peak in SFR would indicate that the predominant process is galaxy-galaxy

harassment, due to other infalling galaxies inducing tidal shocks in the still fairly

intact gas reserves of the galaxies.

Further work shows the SFR is found to be at its lowest in the cluster core

for both giant and dwarf galaxies demonstrating the suppression of the SFR is not

dependent on mass. However, the peak in SFR is seen to be mainly due to dwarf

galaxies, with the dwarf galaxies having in general a higher SFR, consistent with

previous work in the literature.

There is little evidence for a difference in the position of the peak in SFR in

the infall regions of high or low velocity dispersion clusters. This provides further

support for galaxy harassment being the most important process in star formation

properties of galaxies infalling into the cluster, and undermines the importance of

the tidal effect of the dark matter haloes of the clusters involved.

Studies of groups within the filaments show that there is little variation in SFR

with distance for the group galaxies taken from the whole 2dFGRS. This is in con-

trast with the group galaxies within the filaments which again show a peak at a few

virial radii. This would suggest that the the filament environment is dominant over

the group environment with respects to SFR at this distance.

A similar analysis using the 2dFGRS η parameter was also used to investigate

the star formation within a larger ensemble of over 50 filaments of galaxies joining

two clusters. Trends that are consistent with the smaller sample of Pisces-Cetus

filament galaxies are seen, with an increase in SFR at a approximately 1.5 virial

radii from the cluster cores. The results are also confirmed although to a lesser

degree for a more liberally defined sample of over 300 filaments.

A more robust measurement of the SFR was sought to investigate the Shapley

7.2. Future work 143

supercluster region. Here, from 6dF spectra of galaxies in the Shapley supercluster

region, the equivalent width of of the Hα emission line was used to obtain a SFR

for galaxies in the region. Galaxies dominated by active galactic nuclei (AGN)

were removed and corrections applied for dust extinction and the underlying stellar

population. However, due to the lack of spectrophotometric calibrations for the 6dF

data only an uncalibrated SFR could be obtained. There is some evidence for a

peak in star formation at a distance of approximately 2 h−170 Mpc from cluster cores

and suppressed star formation within cluster galaxies in the supercluster, compared

with those not in the supercluster, and those in the field. There appears to be little

variation in the percentage of galaxies that are AGN with distance from cluster cores

but some evidence for a decreasing percentage of passive galaxies with increasing

distance.

7.2 Future work

The SDSS provides a massive repository of data that could be used to study SFR

along filaments of galaxies in a much larger region than the 2dFGRS. We had entered

into a collaboration with Biswajit Pandey and Somnath Bharadwaj with a view

to using their catalogue of filaments in the SDSS (Pandey & Bharadwaj, 2006).

However, we were unable to progress far with this work within the time constraints

of this thesis. The spectroscopic data of the SDSS would allow us to study SFR

with the use of emission lines as in Chapter 6, but with better spectrophotometric

calibrations such that a true SFR could be obtained. In addition the multiple

wavelength band photometry available in the SDSS would allow a study of the

colour magnitude relations of the filament galaxies to investigate the possibility of

an intermediate age stellar population, seen in some field galaxies, being present in

filaments.

Further spectroscopic observations of galaxies at varying distances from cluster

cores would allow a more significant study of the SFR properties in the Shapley

region and reduce the large errors that we currently have. This could also be ex-

panded to gain further observations of the Horologium-Reticulum region which is

7.2. Future work 144

more sparsely covered by 6dF than Shapley. Indeed, it would be very useful to ob-

tain high resolution spectra of the Shapley, Horologium-Reticulum and Pisces-Cetus

supercluster regions, probing deeper into the dwarf galaxy population (MB ≈ −15),

using the Anglo-Australian Telescope 2dF or Magellan IMACS, so that the work

initiated in Chapter 6 can be done properly. With a greater number of galaxies avail-

able, it may also be possible to investigate the SFR along Shapley and Horologium-

Reticulum filaments rather than general spatial relations we have now.

While our results of §4.2.4 showed no relation of the position of the peak in SFR

with the velocity dispersion of the nearest clusters, the results were based on only 4

clusters. A better result could be obtained by using all available redshifts and the

technique used in §3.2 to obtain the velocity dispersions for all the clusters in the 52

filament sample and performing the same split into high and low velocity dispersion

cluster samples.

Bibliography

Abazajian K., et al., 2005, AJ, 129, 1755

Abell G., 1958, ApJS 3, 21

Abell G., 1961 AJ, 66, 607

Abell G., Corwin H., Olowin R., 1989, ApJS 70, 1 (ACO)

Albrecht A., Steinhardt P. J., Turner M. S., Wilczek F., 1982, Physical Review

Letters, 48, 1437

Andernach H., Tago E., Stengler-Larrea E., 1995, Astroph. Lett & Comm. 31, 27

Ashman K. M., Bird C. M., Zepf S. E., 1994, AJ, 108, 2348

Bagchi J., Enßlin T. A., Miniati F., Stalin C. S., Singh M., Raychaudhury S.,

Humeshkar N. B., 2002, New Astronomy, 7, 249

Bahcall N.A., Soneira M., 1984, ApJ, 277, 27

Bahcall N. A., 1988, Annual review of astronomy and astrophysics, 26, 631

Bahcall N. A., Fan X., 1998, ApJ, 504, 1

Bahcall N. A., 2000, Particle Physics and the Universe, Proceedings of Nobel Sym-

posium 109, Haga Slott, Enkping, Sweden, 2000, 85, 32

Baier F.W., Godlowski W., MacGillivray H.T., 2003, A&A, 403, 847

Baldwin J. A., Phillips M. M., Terlevich R., 1981, Astronomical Society of the

Pacific, Publications, 93, 5

145

BIBLIOGRAPHY 146

Balogh M.L., Schade D., Morris S.L., Yee H.K.C., Carlberg R.G., Ellingson E., 1998,

ApJ, 504, L75

Balogh M. L., Morris S. L., Yee H. K. C., Carlberg R. G., Ellingson E., 1999, ApJ,

527, 54

Balogh M., et al., 2004, MNRAS, 348, 1355

Bardelli S., Zucca E., Zamorani G., Moscardini L., Scaramella R., 2000, MNRAS,

312, 540

Bartelmann M., 1996, A&A, 313, 697

Basilakos S., Plionis M., 2004, MNRAS, 349, 882

Benn C.R., 1997, Observational astronomy with the new radio surveys, Conf. Proc.

Astrophysics and Space Science Library 226. Kluwer, Dordrecht

Bennett C. L., et al., 1997, Bulletin of the American Astronomical Society, 29, 1353

Bharadwaj S., Sahni V., Sathyaprakash B. S., Shandarin S. F., Yess C., 2000, ApJ,

528, 21

Bharadwaj S., Bhavsar S. P., Sheth J. V., 2004, ApJ, 606, 25

Bhavsar, S. P. & Splinter, R. J. 1996, MNRAS, 282, 1461

Bhavsar, S. P., & Raychaudhury, S. 2000, Bulletin of the American Astronomical

Society, 32, 1433

Binney J., & Tremaine S., 1987, Galactic Dynamics (Princeton: Princeton Univ.

Press)

Bogart R. S., Wagoner R. V., 1973, ApJ, 181, 609

Bohringer H., et al., 2001, A&A, 369, 826

Bohringer, H., et al. 2000, ApJS, 129, 435

Bohringer, H., et al. 2002, ApJ, 566, 93

BIBLIOGRAPHY 147

Bohringer H., et al., 2004, A&A, 425, 367

Bond J. R., Kofman L., Pogosyan D., 1996, Nature, 380, 603

Bower R. G., Lucey J. R., Ellis R. S., 1992, MNRAS, 254, 601

Brand K., Rawlings S., Hill G. J., Lacy M., Mitchell E., Tufts J., 2003, MNRAS,

344, 283

Breen J., Raychaudhury S., Forman W., Jones C., 1994, ApJ, 424, 59

Brinchmann J., Charlot S., White S. D. M., Tremonti C., Kauffmann G., Heckman

T., Brinkmann J., 2004, MNRAS, 351, 1151

Bruzual A. G., 1983, ApJ, 273, 105

Bruzual G., Charlot S., 2003, MNRAS, 344, 1000

Burles S., Nollett K. M., Turner M. S., 2001, ApJ, 552, L1

Burns J. O., Moody J. W., Brodie J. P., Batuski D. J., 1988, ApJ, 335, 542

Burstein D., Davies R. L., Dressler A., Faber S. M., Lynden-Bell D., 1986, Galaxy

distances and deviations from universal expansion; Proceedings of the NATO

Advanced Research Workshop, Kona, HI, Jan. 13-17, 1986 (A87-27726 11-90).

Dordrecht, D. Reidel Publishing Co., 123

Bushouse H. A., 1987, ApJ, 320, 49

Butcher H., Oemler A., Jr., 1984, ApJ, 285, 426

Calzetti D., 2001, Publications of the Astronomical Society of the Pacific, 113, 1449

Caretta C.A., Maia M.A.G., Kawasaki W., Willmer C.N.A., 2002, ApJ, 123, 1200

Cen R., Ostriker J. P., 1999, ApJ, 514, 1

Chung D.J.J., Kolb E.W., Riotto A., Tkachev I.I., 2000, Physical Review D (Parti-

cles, Fields, Gravitation, and Cosmology), 62, 043508

Colberg J.M. et al., 2000, MNRAS 319, 209

BIBLIOGRAPHY 148

Colberg J. M., Krughoff K. S., Connolly A. J., 2005, MNRAS, 359, 272

Colın P., Avila-Reese V., Valenzuela O., 2001, Astronomical Society of the Pacific

Conference Series, 230, 651

Colless M., et al., 2001, MNRAS, 328, 1039

Colless M. et al.http://msowww.anu.edu.au/2dFGRS/ (astro-ph/0306581)

Couch W.J., Sharples R.M., 1987, MNRAS, 229, 423

Couch W. J., Balogh M. L., Bower R. G., Smail I., Glazebrook K., Taylor M., 2001,

ApJ, 549, 820

Cruddace R., et al., 2002, ApJS, 140, 239

Danese L., de Zotti G., di Tullio G., 1980, A&A, 82, 322

Maddox S. J., Efstathiou G., Sutherland W. J., Loveday J., 1990, MNRAS, 242,

43P

Dalton G.B., Maddox S.J., Sutherland W.J., Efstathiou G., 1997, MNRAS, 289, 263

David L. P., Forman W., Jones C., 1999, ApJ, 519, 533

Davies J. I., Roberts S., Sabatini S., 2005, MNRAS, 356, 794

dell’Antonio I. P., Geller M. J., Fabricant D. G., 1994, AJ, 107, 427

De Propris R., et al., 2002, MNRAS, 329, 87

De Propris R., et al., 2004, MNRAS, 351, 125

de Vaucouleurs G., 1953, AJ, 58, 30

de Vaucouleurs G., 1956, Vistas in Astronomy, 2, 1584

Dressler A., 1980, ApJ, 236, 351

Drinkwater M. J., Parker Q. A., Proust D., Slezak E., Quintana H., 2004, Publica-

tions of the Astronomical Society of Australia, 21, 89

BIBLIOGRAPHY 149

Durret F., Lima Neto G.B., Forman W., Churazov E., 2003, A&A, 403, L29

Ebeling H., Voges W., Bohringer H., Edge A. C., Huchra J. P., Briel U. G., 1996,

MNRAS, 281, 799

Ebeling H., Edge A., Bohringer H., Allen S.W., Crawford C.S., Fabian A.C., Voges

W., Huchra J.P., 1998, MNRAS, 301, 881(BCS)

Ebeling H., Barrett E., Donovan D., 2004, ApJ, 609, L49

Edge A. C., Stewart G. C., 1991, MNRAS, 252, 414

Einasto J., Einasto M., Gramann M., 1989, MNRAS, 238, 155

Einasto J., Gramann M., Saar E., Tago E., 1993, MNRAS, 260, 705

Einasto M., Einasto J., Tago E., Dalton G. B., Andernach H., 1994, MNRAS, 269,

301

Einasto M. Tago M., Jaaniste J., Einasto J., Andernach H., 1997, A&A , 123, 119

Einasto M., Einasto J., Tago E., Muller V., Andernach H., 2001, ApJ, 122, 2222

Einasto M., Jaaniste J., Einasto J., Heinamaki P., Muller V., Tucker D. L., 2003,

A&A, 405, 821

Efstathiou G., Sutherland W. J., Maddox S. J., 1990, Nature, 348, 705

Davis M., Efstathiou G., Frenk C. S., White S. D. M., 1992, Nature, 356, 489

Eke V. R. et al., 2004, MNRAS, 348, 866

Ettori S., Fabian A. C., White D. A., 1997, MNRAS, 289, 787

Fabian A.C., 1991, MNRAS, 253, 29P

Feigelson E. D., Akritas M. G., Rosenberger J. L., 1995, Astronomical Data Analysis

Software and Systems IV, ASP Conference Series , 77, 311

Fleenor M. C., Rose J. A., Christiansen W. A., Hunstead R. W., Johnston-Hollitt

M., Drinkwater M. J., Saunders W., 2005, AJ, 130, 957

BIBLIOGRAPHY 150

Fleenor M. C., Rose J. A., Christiansen W. A., Johnston-Hollitt M., Hunstead

R. W., Drinkwater M. J., Saunders W., 2006, AJ, 131, 1280

Frisch P., Einasto J., Einasto M., Freudling W.,Fricke K.J., Gramann M., Saar V.,

Toomet O., 1995, A&A 296, 611

Fritz A., Ziegler B. L., 2003, Astronomische Nachrichten, Supplementary Issue

3, Short Contributions of the Annual Scientific Meeting of the Astronomische

Gesellschaft in Freiburg, September 15-20, 2003 , 324, 56

Fujita Y., 1998, ApJ, 509, 587

Fujita Y., Sarazin C.L., Kempner J.C., Rudnick L., Slee O.B., Roy A.L., Andernach

H., Ehle M., 2002, ApJ, 575, 764

Fujita Y., Sarazin C.L., Kempner J.C., Rudnick L., Slee O.B., Roy A.L., Andernach

H., Ehle M., 2004, ApJ, 616, 157

Fujita Y., Goto T., 2004, PASJ, 56, 621

Fukuda Y., et al., 1998, Physical Review Letters, 81, 1562

Gastaldello F., Ettori S., Molendi S., Bardelli S., Venturi T., Zucca E., 2003, A&A,

411, 21

Geller M. J., Huchra J. P., 1989, Science, 246, 897

Gallagher J. S., Hunter D. A., Tutukov A. V., 1984, ApJ, 284, 544

Gavazzi G., Catinella B., Carrasco L., Boselli A., Contursi A., 1998, AJ, 115, 1745

Gaztanaga E., 2002, MNRAS, 333, L21

Gilfanov M., Grimm H.-J., Sunyaev R., 2004, MNRAS, 347, L57

Gill S. P. D., Knebe A., Gibson B. K., 2005, MNRAS, 356, 1327

Giovannini, G.; Feretti, L., 2000, New Astronomy, 5, 335

BIBLIOGRAPHY 151

Girardi M., Giuricin G., Mardirossian F., Mezzetti M., Boschin W., 1998, ApJ, 505,

74

Gladders M. D., Lopez-Cruz O., Yee H. K. C., Kodama T., 1998, ApJ, 501, 571

Glazebrook K., Offer A. R., Deeley K., 1998, ApJ, 492, 98

Gnedin O. Y., 2003, ApJ, 582, 141

Gomez P. L., et al., 2003, ApJ, 584, 210

Goto T., et al., 2003, Astronomical Society Japan Publications, 55, 739

Gramann M., Hutsi G., 2000, MNRAS, 316, 631

Gramann M., Hutsi G., 2001, MNRAS, 327, 538

Gramann M., Suhhonenko I., MNRAS, 2002, 337, 1417

Grimm H.-J., Gilfanov M., Sunyaev R., 2003, MNRAS, 339, 793

Gunn J. E., Gott J. R. I., 1972, ApJ, 176, 1

Guzman R., Lucey J. R., Carter D., Terlevich R. J., 1992, MNRAS, 257, 187

Haines C. P., La Barbera F., Mercurio A., Merluzzi P., Busarello G., 2006, ApJ,

647, L21

Haines C. P., Merluzzi P., Mercurio A., Gargiulo A., Krusanova N., Busarello G.,

La Barbera F., Capaccioli M., 2006, MNRAS, 371, 55

Hambly N. C., et al., 2001, MNRAS, 326, 1279

Hauser M. G., Peebles P. J. E., 1973, ApJ, 185, 757

Hernquist L., 1990, ApJ, 356, 359

Hoessel J.G., Gunn J.E., Thuan T.X., 1980 ApJ, 241, 486

Hoffman Y., 2001, Mining the Sky: Proceedings of the MPA/ESO/MPE Workshop

Held at Garching, Germany, July 31 - August 4, 2000, ESO ASTROPHYSICS

SYMPOSIA. ISBN 3-540-42468-7 , 223

BIBLIOGRAPHY 152

Hogg, D. W. 1999, ArXiv Astrophysics e-prints, arXiv:astro-ph/9905116

Hopkins A. M., et al., 2003, ApJ, 599, 971

Horner, D., 2001, Ph.D. Thesis, University of Maryland

Howard S., Byrd G. G., 1990, AJ, 99, 1798

Hudson M. J., Smith R. J., Lucey J. R., Branchini E., 2004, MNRAS, 352, 61

Jaffe W., 1983, MNRAS, 202, 995

Jarrett T. H., Chester T., Cutri R., Schneider S., Skrutskie M., Huchra J. P., 2000,

AJ, 119, 2498

Jenkins A., et al., 1998, ApJ, 499, 20

Jones C., Forman W., 1999, ApJ, 511, 65

Jones D. H., et al., 2004, MNRAS, 355, 747

Jones D. H., Saunders W., Read M., Colless M., 2005, PASA, 22, 277

Kaiser N., 1984, ApJ, 284, L9

Kaiser N., 1987, MNRAS, 227, 1

Kaldare R., Colless M., Raychaudhury S., Peterson B. A., 2003, MNRAS, 339, 652

Katgert P., Mazure A., den Hartog R., Adami C., Biviano A., Perea J., 1998, A&AS,

129, 399

Kauffmann G., et al., 2003, MNRAS, 346, 1055

Kauffmann G., White S. D. M., Heckman T. M., Menard B., Brinchmann J., Charlot

S., Tremonti C., Brinkmann J., 2004, MNRAS, 353, 713

Kawasaki W., Shimasaku K.,Doi M., Okamura S., 1998, A&AS, 130, 567

Kempner J.C., Sarazin C.L., 2002, ApJ, 579, 236

BIBLIOGRAPHY 153

Kenney J. D. P., 1994, Astronomical Society of the Pacific Conference Series, 59,

282

Kennicutt R. C., 1983, ApJ, 272, 54

Kennicutt R. C., Jr., Roettiger K. A., Keel W. C., van der Hulst J. M., Hummel

E., 1987, AJ, 93, 1011

Kennicutt R. C., Jr., 1989, ApJ, 344, 685

Kennicutt R. C., Jr., 1992, ApJ, 388, 310

Kennicutt R. C., Jr., Schweizer F., Barnes J. E., Friedli D., Martinet L., Pfenniger

D., 1998, Galaxies: Interactions and Induced Star Formation, Saas-Fee Advanced

Course 26. Lecture Notes 1996. Swiss Societyfor Astrophysics and Astronomy,

ISBN: 3-540-63569-6

Kennicutt R. C., 1998, ARA&A, 36, 189

Kewley L. J., Heisler C. A., Dopita M. A., Lumsden S., 2001, ApJS, 132, 37

King I., 1962, AJ, 67, 471

Kolatt T., Dekel A., Ganon G., Willick J.A., 1996 ApJ, 458, 419

Kolokotronis V., Basilakos S., Plionis M., 2002, MNRAS, 331, 1020

Koranyi D.M., Geller M.J., 2000, AJ, 119, 44

Kull A., Boringer H., 1999, A&A, 341, 23

Lacy M., 2000, ApJ, 536, L1

Lahav O., et al., 2002, MNRAS, 333, 961

Lake, G., & Moore, B. 1999, IAU Symp. 186: Galaxy Interactions at Low and High

Redshift, 186, 393

Larson R. B., Tinsley B. M., Caldwell C. N., 1980, ApJ, 237, 692

Ledlow M.J., Voges W., Owen F.N., Burns J.O., 2003, ApJ, 126, 2740

BIBLIOGRAPHY 154

Le Fevre O., et al., 2004, A&A, 417, 839

Lewis I., et al., 2002, MNRAS, 334, 673

Lidsey J. E., 1994, MNRAS, 266, 489

Lin D. N. C., Pringle J. E., Rees M. J., 1988, ApJ, 328, 103

Liu C. T., Kennicutt R. C., 1995, ApJ, 450, 547

Lucey J. R., Dickens R. J., Mitchell R. J., Dawe J. A., 1983, MNRAS, 203, 545

Lumsden S.L., Nichol R.C., Collins C.A., Guzzo L., 1992, MNRAS, 258, 1

Lumsden S.L., Collins C.A., Nichol R.C., Eke V.R., Guzzo L., 1997, MNRAS, 290,

119

Madgwick D.S., et al.(the 2dFGRS Team), 2002, MNRAS, 333, 133

Madgwick D.S., Somerville R., Lahav O., Ellis R., 2003, MNRAS, 343, 871

Mahdavi A., Geller M. J., Fabricant D. G., Kurtz M. J., Postman M., McLean B.,

1996, AJ, 111, 64

Menanteau F., Ford H. C., Motta V., Benıtez N., Martel A. R., Blakeslee J. P.,

Infante L., 2006, AJ, 131, 208

Margoniner V. E., de Carvalho R. R., Gal R. R., Djorgovski S. G., 2001, ApJ, 548,

L143

Mathis H., White S.D.M., 2002, MNRAS, 337, 1193

Matkovic, A., & Guzman, R. 2003, Bulletin of the American Astronomical Society,

36, 590

Mazure, A., et al.1996, A&A, 310, 31

Miller N. A., Owen F. N., 2002, AJ, 124, 2453

Miller C. J., Nichol R. C., Gomez P. L., Hopkins A. M., Bernardi M., 2003, ApJ,

597, 142

BIBLIOGRAPHY 155

Miller L., Croom S. M., Boyle B. J., Loaring N. S., Smith R. J., Shanks T., Outram

P., 2004, MNRAS, 355, 385

Mohr J. J., Geller M. J., Wegner G., 1996, AJ, 112, 1816

Moore B., Katz N., Lake G., Dressler A., Oemler A., Jr., 1996, Nature, 379, 613

Moore B., Lake G., Quinn T., Stadel J., 1999, MNRAS, 304, 465

Moran S. M., Ellis R. S., Treu T., Smail I., Dressler A., Coil A. L., Smith G. P.,

2005, ApJ, 634, 977

Moustakas J., Kennicutt R. C., Jr., Tremonti C. A., 2006, ApJ, 642, 775

Mulchaey, J.S., Zabludoff A.I., 1998, ApJ, 496, 73

Mulchaey, J. S., Davis, D. S., Mushotzky, R. F., & Burstein, D. 2003, ApJS, 145,

39

Navarro J. F., Frenk C. S., White S. D. M., 1995, MNRAS, 275, 720

Navarro, J.F., Frenk, C. S., & White, S. D. M. 1996, ApJ, 462, 563

Noguchi M., 1988, A&A, 203, 259

Norberg P., et al., 2001, MNRAS, 328, 64

Olson K. M., Kwan J., 1990, ApJ, 349, 480

Osmond J., Ponman T., 2004, MNRAS, 350, 1511

O’Sullivan E., Forbes D. A., Ponman T. J., 2001, MNRAS, 328, 461

Pandey B., Bharadwaj S., 2005, MNRAS, 357, 1068

Pandey B., Bharadwaj S., 2006, MNRAS, 988

Peebles P.J.E., Schramm D.N., Turner E.L., Kron R.G., 1991, Nature, 352, 769

Peacock J.A., Nicholson D., 1991, MNRAS, 253, 307

Peacock J. A., et al., 2001, Nature, 410, 169

BIBLIOGRAPHY 156

Pedersen K., Rasmussen J., Sommer-Larsen J., Toft S., Benson A. J., Bower R. G.,

2006, NewA, 11, 465

Peebles P. J. E., 1982, ApJ, 263, L1

Percival W. J., et al., 2001, MNRAS, 327, 1297

Perlmutter S., et al., 1999, ApJ, 517, 565

Petrosian V., 1976, ApJ, 209, L1

Pimbblet K. A., Drinkwater M. J., Hawkrigg M. C., 2004, MNRAS, 354, L61

Plummer H. C., 1911, MNRAS, 71, 460

Popesso P., Biviano A., Bohringer H., Romaniello M., Voges W., 2005, A&A, 433,

431

Poggianti B. M., et al., 2006, ApJ, 642, 188

Ponman T. J., Bourner P. D. J., Ebeling H., Bohringer H., 1996, MNRAS, 283, 690

Ponman T. J., Cannon D. B., Navarro J. F., 1999, Nature, 397, 135

Press W. H., Schechter P., 1974, ApJ, 187, 425

Press W. H., Teukolsky S. A., Vetterling W. T. & Flannery B. P., 1992, Numerical

Recipes in Fortran 2nd ed. (Cambridge: Cambridge University Press)

Proust D., Quintana H., Mazure A., da Souza R., Escalera E., Sodre Jr, L. and

Capelato H.V., 1992, A&A, 258, 243

Proust D., et al., 2006, A&A, 447, 133

Radburn-Smith D. J., Lucey J. R., Hudson M. J., 2004, MNRAS, 355, 1378

Radburn-Smith D. J., Lucey J. R., Woudt P. A., Kraan-Korteweg R. C., Watson

F. G., 2006, MNRAS, 369, 1131

Ranalli P., Comastri A., Setti G., 2003, A&A, 399, 39

BIBLIOGRAPHY 157

Rasmussen J., Ponman T. J., Mulchaey J. S., 2006, MNRAS, 370, 453

Ravindranath S., et al., 2006, Galaxy Evolution Across the Hubble Time, Interna-

tional Astronomical Union. Symposium, 235

Raychaudhury S., 1989, Nature, 342, 251

Raychaudhury S., 1989, PhD Thesis, University of Cambridge

Raychaudhury S., Fabian A.C., Edge A.C., Jones C., Forman W., 1991, MNRAS

248, 101

Raychaudhury S., Bhavsar S.P., Huchra J.P., 2007, to be published

Refregier A., Valtchanov I., Pierre M., 2002, A&A, 390 ,1

Reiprich, T.H., Bohringer H., 2002, ApJ, 567, 716

Rojas R. R., Vogeley M. S., Hoyle F., Brinkmann J., 2005, ApJ, 624, 571

Rose J. A., Gaba A. E., Christiansen W. A., Davis D. S., Caldwell N., Hunstead

R. W., Johnston-Hollitt M., 2002, AJ, 123, 1216

Rubin V. C., Ford W. K. J., 1970, ApJ, 159, 379

Ruderman J. T., Ebeling H., 2005, ApJ, 623, L81

Ruffle P. M. E., Zijlstra A. A., Walsh J. R., Gray M. D., Gesicki K., Minniti D.,

Comeron F., 2004, MNRAS, 353, 796

Scaramella R., Baiesi-Pillastrini G., Chincarini G., Vettolani G., Zamorani G., 1989,

Nature, 338, 562

Schwope A., Hasinger G., Lehmann I., Schwarz R., Brunner H., Neizvestny

S., Ugryumov A., Balega Yu., Trmper J., Voges W., 2000, Astronomische

Nachrichten, 321, 1, 1

Sekiguchi K., Wolstencroft R. D., 1993, MNRAS, 263, 349

Shandarin S. F., Sheth J. V., Sahni V., 2004, MNRAS, 353, 162

BIBLIOGRAPHY 158

Shapley H., 1930, Ball Harvard Observatory Bulletin, 874, 9

Shapley H., 1930, Harvard College Observatory Circlular, 350, 1

Shapley H., 1933, Proc. Nat. Acad. Sci. USA 19, 591

Shapley H., 1935, Annals of the Astronomical Observatory of Harvard College, 88,

105

Shen, Mulchaey, Raychaudhury, Rasmussen, Ponman, 2007, Submitted to ApJ let-

ters

Simon P., Schneider P., Erben T., Schirmer M., Wolf C., Meisenheimer K., 2004,

Proceedings of ”Baryons in Dark Matter Halos”. Novigrad, Croatia, 5-9 Oct 2004.

Editors: R. Dettmar, U. Klein, P. Salucci. Published by SISSA, Proceedings of

Science, 97

Slee O. B., Roy A. L., Murgia M., Andernach H., Ehle M., 2001, AJ, 122, 1172

Smoot G. F., et al., 1992, ApJ, 396, L1

Spergel D. N., et al., 2003, ApJS, 148, 175

Springel V., Yoshida N., White S.D.M., 2001 New Astronomy, 6, 79

Springel V., 2005, MNRAS, 364, 1105

Storey P. J., Hummer D. G., 1995, MNRAS, 272, 41

Struble M.F., Rood, H.J., 1999, ApJS, 125, 35

Struck-Marcell C., Scalo J. M., 1987, ApJS, 64, 39

Tremonti C. A., et al., 2004, ApJ, 613, 898

Tully R. B., 1986, ApJ, 303, 25

Tully R. B., 1987, ApJ, 323, 1

Tully R. B., 1988, International Astronomical Union Symposia, 130, 243

BIBLIOGRAPHY 159

van Dokkum P. G., Franx M., 2001, ApJ, 553, 90

van Dokkum P. G., Stanford S. A., 2003, ApJ, 585, 78

Veilleux S., Osterbrock D. E., 1987, ApJS, 63, 295

Veilleux S., Cecil G., Bland-Hawthorn J., Tully R. B., Filippenko A. V., Sargent

W. L. W., 1994, ApJ, 433, 48

Viana P. T. P., Nichol R. C., Liddle A. R., 2002, ApJ, 569, L75

White S. D. M., Frenk C. S., Davis M., 1983, ApJ, 274, L1

White S. D. M., Davis M., Frenk C. S., 1984, MNRAS, 209, 27P

White M., 2006, http://astro.berkeley.edu/ mwhite/modelcmp.html

Wu X.P., Xue, Y.J., 1999, ApJ, 524, 22

Xu C., Sulentic J. W., 1991, ApJ, 374, 407

Xue Y., Wu X., 2000, ApJ, 538, 65

Zel’Dovich Y. B., 1970, A&A, 5, 84

Zeng N., White S. D. M., 1991, ApJ, 374, 1

Zucca E., Zamorani G., Scaramella R., Vettolani G., 1993, ApJ, 407, 470

Zwicky F., 1933, Helvetica Physica Acta, 6, 110

Zwicky F., Herzog E., Wild P., Karpowicz M., Kowal C.T., 1961-1968, Catalogue of

Galaxies and Clusters of Galaxies (California Institute of Technology, Pasadena)

Appendix A

Optical Surface brightness fits to

clusters in the Pisces-Cetus

supercluster

In section 3.2.1 we fitted the Navarro Frenk White (NFW) X-ray surface brightness

model to optical surface brightness profiles of clusters of galaxies in superclusters,

using SuperCOSMOS data (UK Schmidt blue (Bj)). This enables us to obtain an

estimate of the virial mass of each of the clusters. This appendix contains plots of

the surface brightness profiles of the clusters of the Pisces-Cetus supercluster and

the best fit line of the NFW model to the curves.

Figure A.1: Optical (Bj) radial surface brightness profiles with the best-fit projected NFW

model (Eq. 3.7) superposed for A0014, A0027 and A0074. Member galaxies are binned in annuli

around the cluster centre, such that each annulus contains an equal number of galaxies.

160

Appendix A. Optical Surface brightness fits to clusters (P-C) 161


model (Eq. 3.7) superposed for A0085, A0086 and A0087. Member alaxies are binned in annuli








Appendix A. Optical Surface brightness fits to clusters (P-C) 162





model (Eq. 3.7) superposed for A2800, A2824, and A4053. Member galaxies are binned in annuli



model (Eq. 3.7) superposed for A2794, S1136 and S1155. Member galaxies are binned in annuli

around the cluster centre, such that each annulus has a constant radius.

Appendix B


clusters in the

Horologium-Reticulum

supercluster




estimate of the virial mass of each of the clusters. This appendix contains plots of the

surface brightness profiles of the clusters of the Horologium-Reticulum supercluster

and the best fit line of the NFW model to the curves.

Figure B.1: Optical (Bj) radial surface brightness profiles with the best-fit projected NFW


around the cluster centre, such that each annulus has a constant number of galaxies.

163

Appendix B. Optical Surface brightness fits to clusters (H-R) 164












model (Eq. 3.7) superposed for A3312. Member galaxies are binned in annuli around the cluster

centre, such that each annulus has a constant number of galaxies.

Appendix C


clusters in the Shapley

supercluster




estimate of the virial mass of each of the clusters. This appendix contains plots of

the surface brightness profiles of the clusters of the Shapley supercluster and the

best fit line of the NFW model to the curves.

Figure C.1: Optical (Bj) radial surface brightness profiles with the best-fit projected NFW


around the cluster centre, such that each annulus has a onstant radius.

168

Appendix C. Optical Surface brightness fits to clusters (S) 169


model (Eq. 3.7) superposed for A1736, A3528N and A3528S. Member galaxies are binned in annuli







around the cluster centre, such that each annulus has a costant number of galxies in it.






model (Eq. 3.7) superposed for SC1327 and SC1329. Member galaxies are binned in annuli around

the cluster centre, such that each annulus has a constant number of galaxies.

Appendix D

X-ray analysis of the Pisces-Cetus

supercluster

D.1 X-Ray observations

For the clusters that form the Pisces-Cetus supercluster (see §3.1.1), relevant X-ray

observations were taken from the data archives of the respective observatories, via

the High Energy Astrophysics Science Archive Research Center (HEASARC). The

X-ray observations were used to confirm the presence and location of the cluster,

whenever possible and determine the centre of the cluster. Where X-ray observa-

tions were available from multiple sources, ROSAT PSPC pointed observations were

preferentially used. If these were not available, ROSAT All-Sky Survey data (short

PSPC observations) or Einstein data were used.

D.1.1 ROSAT archival pointed observations

Where archival data were available for a cluster, reduction was performed using

the Asterix software package (http://www.sr.bham.ac.uk/asterix-docs). The initial

data were background subtracted, using backgrounds with point sources extracted.

The background was then flattened and used to estimate vignetting and the image

adaptively smoothed using asmooth. An estimate of the variance was found using

smooth on the largest Gaussian used in asmooth, and then this variance array

172

D.1. X-Ray observations 173

used to form a background error map. The smoothed image was then background

subtracted and divided by the background standard deviation (σ) map, to get the

number of σ above the background map. This does mean that the significance of

contours in the less heavily smoothed regions is actually an over-estimate of the

significance. The contours were then overlaid on to an optical DSS image. Contour

levels are at 5 10 20 40 ... σ above the background. The overlays for the clusters

with pointed ROSAT data can be seen in Fig. D.1.

D.1.2 Rosat all-sky Survey and Einstein IPC observations

For the clusters for which pointed X-ray observations were not available in the

archives, the ROSAT all-sky (RASS) data were inspected. If an inspection by eye

of the image, reconstructed from the event map in the energy range of 0.1-2.4 kev,

showed an extended X-ray source in the vicinity of the cluster coordinates, an X-ray

contour overlay was created using the GAIA software package. The X-ray data was

convolved with an elliptical Gaussian function and overlayed on a 20 arcminute DSS

image of centred on the cluster centre. The contour levels were linear, and chosen

to obtain a sensible contour image. The overlays for the clusters with RASS data

can be seen in Fig. D.1. A similar method to the above was used for Einstein IPC

data, contour overlays obtained and these can also be found in Fig. D.1.

D.1.3 The LX–σ relation

Theory

If it is assumed that hot gas traces the gravitating mass profile and radiates most

of its energy through bremsstrahlung radiation then,

Lx ∝ f 2gasT

2, (D.1.1)

(Ponman, Cannon, & Navarro, 1999) where fgas is the gas fraction or the ratio of the

gas to the total mass and T is the X-ray temperature. In the case of self similarity,

the gas fraction is assumed to be constant. Thus the relation becomes,

Lx ∝ T 2, (D.1.2)


Figure D.1: (Top row) X-ray contours from pointed ROSAT PSPC observations,

superposed on optical (Blue) DSS images of the clusters Abell 85, Abell 133 and

Abell 2734. (Middle row) Similar images of Abell 14 (RASS), Abell 74 & Abell 117

(Einstein IPC), Abell 151 (RASS), and (Bottom row) of Abell 2716, Abell 2794,

Abell 2800, and Abell S1136 (all RASS).


If the virial theorem holds it follows that

σ2clus ∝

M

Rv, (D.1.3)

where σclus is the line of sight velocity dispersion, M is the mass of the cluster and

Rv is the virial radius. Hence,

σclus ∝ T 0.5, (D.1.4)

This gives rise to,

Lx ∝ σ4clus, (D.1.5)

Therefore, we would expect a gradient of 4 to the log Lx–log σ relation of our

clusters if the above assumptions hold.

D.1.4 Pisces-Cetus supercluster results

X-ray luminosities (Lx) for the individual clusters from the literature (See Table 3.1)

were converted into values of Lx in the bolometric energy range and normalised

for the Hubble constant used. The conversion was performed in PIMMS using a

Raymond-Smith model with a temperature estimated from the velocity dispersion-

temperature relation of Osmond & Ponman (2004) and a suitable H I Column Den-

sity using the HESEARC tools (http://heasarc.gsfc.nasa.gov/cgi-bin/Tools/w3nh/

w3nh.pl).

The X-ray luminosity and velocity dispersion for those of our clusters which have

both values are plotted in Fig.D.2. The line of best fit for our data gives log Lx =

6.67 log σ+24.84. We compare our results with those of Wu & Xue (1999), who used

a sample of 156 clusters from literature and obtained the relation, Lx = 10−14.57σ5.24.

For groups, Osmond & Ponman (2004) used ROSAT data for a sample of 60 groups

and obtained the relation, log Lx = 3.1 log σ−2 log(h)+34.27. However, Mulchaey &

Zabludoff (1998) found the relation log Lx = 4.29 log σ−2 log(h)+31.61 for a sample

of 12 groups with ROSAT data. These three relations are plotted for comparison

with our own in Fig. D.2 along with the data points of Osmond & Ponman (2004).

A Kolmogorov-Smirnov (KS) test was performed to find the significance of the

differences between each of the above relations and our own. It was found that the


Figure D.2: The relationship between Lx and σ for clusters in the Pisces-Cetus supercluster,

with available X-ray data. Cross symbols are our cluster data points while the open circle symbols

are the points for (Osmond & Ponman, 2004) for groups. Solid= best fit to the data points, dot-

dash=(Wu & Xue, 1999), dashed=(Mulchaey & Zabludoff, 1998), dash-dot-dot-dot=(Osmond &

Ponman, 2004) All values of Lx are in the bolometric energy range

probability that the Mulchaey & Zabludoff (1998) relation was drawn from the same

Lx–σ distribution as our own relation is 21.8 %. However, the relation of (Osmond

& Ponman, 2004) was found to have only a 1.8 % probability of being drawn from

the same Lx–σ distribution as our relation. The relatively low probability for the

Osmond & Ponman (2004) relation implies a possible steepening of the LX − σ

relation for clusters. This is in agreement with the results of Xue & Wu (2000) who

also found a steepening for the cluster relation.

The relation of Wu & Xue (1999) was found to have a 54.2% probability of being

drawn from the same distribution as our own relation showing a fair agreement

between the two. This would suggest little difference in the LX–σ relation of clusters

inside and out of a supercluster.

Discussion

From Eq.D.1.5, we would expect a gradient of 4 to the Lx–σ relation of our clusters.

However, our line of best fit is seen to have a steeper gradient of 5.33. This would be

consistent with the presence of pre-heating of the Intergalactic Medium, which could


systematically reduce the luminosity of the clusters, with a greater effect on the lower

mass clusters. A possible mechanism for the pre-heating would be the shocking of

the intergalactic medium during the formation of the large scale filaments, present

in the supercluster region, as suggested by Cen & Ostriker (1999).

Our results also show that clusters in the Pisces-Cetus supercluster have a steeper

Lx–σ relation than for groups not in a supercluster. However, there is no signifi-

cant difference in the relation for clusters that are in the Pisces-Cetus supercluster

and clusters which are not in a superluster. The flattening of the Lx–σ relation

for groups has been covered extensively in papers such as dell’Antonio, Geller, &

Fabricant (1994); Ponman et al. (1996); Xue & Wu (2000). Ponman et al. (1996)

find that their flattening of their Lx–σ relation for groups is not statistically signifi-

cant and attribute the flattening seen in dell’Antonio, Geller, & Fabricant (1994) to

the additional X-ray emission of individual galaxies, which had not been removed.

As the contribution of the individual galaxies to the group emission has not been

removed for all of our data points taken from the literature, this may be the reason

for our flattening of the Lx–σ relation for groups.

In addition the method of conversion to bolometric luminosities, based on an

uncertain temperature estimate, also reduces the validity of the comparison. Due to

the lack of a measured temperature for some clusters estimates were found using the

velocity dispersion-temperature relation of Osmond & Ponman (2004). Therefore,

the X-ray luminosities derived from these estimates are slightly dependent on the

velocity dispersion for the cluster. We therefore decided not to include this analysis

in our published paper, but include it in this dissertation as evidence of substantial

exploratory work undertaken in course of this investigation.

Appendix E

The 2dFGRS “clean sample” of

filaments

In section 5.3.1 we describe the 52 filaments that make up the 2dFGRS “clean

sample” (see Table 5.2). This appendix contains plots of the spatial distribution of

the galaxies that form each of the filaments in the “clean sample” and a plot of the

mean η and mean percentage of passive galaxies as a function of distance from the

nearest cluster for the filament galaxies.

Figure E.1: Galaxy position, mean η and mean percentage of passive galaxies in the filaments

joining the clusters: APMCC 0094 and EDCC 0457. Cluster galaxies as defined in §5.3.1 are shown

in red.

178

Appendix E. The 2dFGRS “clean sample” of filaments 179


joining the clusters: Abell 1411 Abell 1407, Abell 1419 Abell 1364, Abell 1620 Abell 1663, Abell

1692 Abell 1663 and Abell 2493 EDCC 0215. Cluster galaxies as defined in §5.3.1 are shown in

red.



joining the clusters: Abell 2553 EDCC 0275, Abell 2601 Abell 4009, Abell 2734 EDCC 0445, Abell

2741 APMCC 0039 and Abell 2741 APMCC 0051. Cluster galaxies as defined in §5.3.1 are shown

in red.



joining the clusters: Abell 2780 APMCC 0039 Abell 2814 Abell 2829, Abell 2829 Abell 0118, Abell

2829 EDCC 0511 and Abell 2878 EDCC 0511. Cluster galaxies as defined in §5.3.1 are shown in

red.



joining the clusters: Abell 2915 EDCC 0581 Abell 2943 APMCC 0222, Abell 2961 APMCC 0245,

Abell 2967 Abell 2972 and Abell 2981 Abell 2999. Cluster galaxies as defined in §5.3.1 are shown

in red.



joining the clusters: Abell 3980 EDCC 0268, EDCC 0217 EDCC 0202, EDCC 0365 Abell S1155,

EDCC 0445 APMCC 0094 and EDCC 0457 EDCC 0445. Cluster galaxies as defined in §5.3.1 are

shown in red.



joining the clusters: EDCC 0465 Abell 2780, EDCC 0465 Abell 2814, EDCC 0517 EDCC 0511,

Abell S0333 Abell 3094 and EDCC 0119 Abell 3837. Cluster galaxies as defined in §5.3.1 are shown

in red.



joining the clusters: EDCC 0057 Abell 3837, EDCC 0057 APMCC 0721, Abell 3878 Abell 3892,

EDCC 0230 APMCC 0827 and APMCC 0827 Abell 3892. Cluster galaxies as defined in §5.3.1 are

shown in red.



joining the clusters: EDCC 0128 Abell 3880, Abell 3959 APMCC 0853, Abell S1075 APMCC 0167,

EDCC 0457 Abell 2794, EDCC 0492 Abell 2804. Cluster galaxies as defined in §5.3.1 are shown

in red.



joining the clusters: EDCC 0202 EDCCC 0187, EDCC 0187 APMCC 0810, EDCC 0317 APMCC

4011, EDCC 0323 APMCC 4012 and Abell 3854 Abell 3844. Cluster galaxies as defined in §5.3.1

are shown in red.



joining the clusters: Abell S1064 EDCCC 0153, Abell 2967 EDCCC 2981, EDCC 0239 APMCC

0853, EDCC 0248 Abell 3959 and APMCC 0167 Abell S0160. Cluster galaxies as defined in §5.3.1

are shown in red.



joining the clusters: APMCC 0869 and APMCC 0840. Cluster galaxies as defined in §5.3.1 are

shown in red.

the properties of galaxies in supercluster filamentsetheses.bham.ac.uk/986/1/porter07phd.pdfthe...

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